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Publisher: Elsevier   (Total: 3175 journals)

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Showing 1 - 200 of 3175 Journals sorted alphabetically
A Practical Logic of Cognitive Systems     Full-text available via subscription   (Followers: 9)
AASRI Procedia     Open Access   (Followers: 14)
Academic Pediatrics     Hybrid Journal   (Followers: 30, SJR: 1.402, h-index: 51)
Academic Radiology     Hybrid Journal   (Followers: 22, SJR: 1.008, h-index: 75)
Accident Analysis & Prevention     Partially Free   (Followers: 87, SJR: 1.109, h-index: 94)
Accounting Forum     Hybrid Journal   (Followers: 25, SJR: 0.612, h-index: 27)
Accounting, Organizations and Society     Hybrid Journal   (Followers: 35, SJR: 2.515, h-index: 90)
Achievements in the Life Sciences     Open Access   (Followers: 5)
Acta Anaesthesiologica Taiwanica     Open Access   (Followers: 6, SJR: 0.338, h-index: 19)
Acta Astronautica     Hybrid Journal   (Followers: 386, SJR: 0.726, h-index: 43)
Acta Automatica Sinica     Full-text available via subscription   (Followers: 2)
Acta Biomaterialia     Hybrid Journal   (Followers: 27, SJR: 2.02, h-index: 104)
Acta Colombiana de Cuidado Intensivo     Full-text available via subscription   (Followers: 2)
Acta de Investigación Psicológica     Open Access   (Followers: 3)
Acta Ecologica Sinica     Open Access   (Followers: 8, SJR: 0.172, h-index: 29)
Acta Haematologica Polonica     Free   (Followers: 1, SJR: 0.123, h-index: 8)
Acta Histochemica     Hybrid Journal   (Followers: 3, SJR: 0.604, h-index: 38)
Acta Materialia     Hybrid Journal   (Followers: 243, SJR: 3.683, h-index: 202)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5, SJR: 0.615, h-index: 21)
Acta Mechanica Solida Sinica     Full-text available via subscription   (Followers: 9, SJR: 0.442, h-index: 21)
Acta Oecologica     Hybrid Journal   (Followers: 10, SJR: 0.915, h-index: 53)
Acta Otorrinolaringologica (English Edition)     Full-text available via subscription  
Acta Otorrinolaringológica Española     Full-text available via subscription   (Followers: 2, SJR: 0.311, h-index: 16)
Acta Pharmaceutica Sinica B     Open Access   (Followers: 1)
Acta Poética     Open Access   (Followers: 4)
Acta Psychologica     Hybrid Journal   (Followers: 25, SJR: 1.365, h-index: 73)
Acta Sociológica     Open Access  
Acta Tropica     Hybrid Journal   (Followers: 6, SJR: 1.059, h-index: 77)
Acta Urológica Portuguesa     Open Access  
Actas Dermo-Sifiliograficas     Full-text available via subscription   (Followers: 3)
Actas Dermo-Sifiliográficas (English Edition)     Full-text available via subscription   (Followers: 2)
Actas Urológicas Españolas     Full-text available via subscription   (Followers: 3, SJR: 0.383, h-index: 19)
Actas Urológicas Españolas (English Edition)     Full-text available via subscription   (Followers: 1)
Actualites Pharmaceutiques     Full-text available via subscription   (Followers: 6, SJR: 0.141, h-index: 3)
Actualites Pharmaceutiques Hospitalieres     Full-text available via subscription   (Followers: 3, SJR: 0.112, h-index: 2)
Acupuncture and Related Therapies     Hybrid Journal   (Followers: 6)
Acute Pain     Full-text available via subscription   (Followers: 14)
Ad Hoc Networks     Hybrid Journal   (Followers: 11, SJR: 0.967, h-index: 57)
Addictive Behaviors     Hybrid Journal   (Followers: 15, SJR: 1.514, h-index: 92)
Addictive Behaviors Reports     Open Access   (Followers: 7)
Additive Manufacturing     Hybrid Journal   (Followers: 9, SJR: 1.039, h-index: 5)
Additives for Polymers     Full-text available via subscription   (Followers: 22)
Advanced Cement Based Materials     Full-text available via subscription   (Followers: 3)
Advanced Drug Delivery Reviews     Hybrid Journal   (Followers: 135, SJR: 5.2, h-index: 222)
Advanced Engineering Informatics     Hybrid Journal   (Followers: 11, SJR: 1.265, h-index: 53)
Advanced Powder Technology     Hybrid Journal   (Followers: 16, SJR: 0.739, h-index: 33)
Advances in Accounting     Hybrid Journal   (Followers: 8, SJR: 0.299, h-index: 15)
Advances in Agronomy     Full-text available via subscription   (Followers: 12, SJR: 2.071, h-index: 82)
Advances in Anesthesia     Full-text available via subscription   (Followers: 27, SJR: 0.169, h-index: 4)
Advances in Antiviral Drug Design     Full-text available via subscription   (Followers: 2)
Advances in Applied Mathematics     Full-text available via subscription   (Followers: 10, SJR: 1.054, h-index: 35)
Advances in Applied Mechanics     Full-text available via subscription   (Followers: 10, SJR: 0.801, h-index: 26)
Advances in Applied Microbiology     Full-text available via subscription   (Followers: 22, SJR: 1.286, h-index: 49)
Advances In Atomic, Molecular, and Optical Physics     Full-text available via subscription   (Followers: 14, SJR: 3.31, h-index: 42)
Advances in Biological Regulation     Hybrid Journal   (Followers: 4, SJR: 2.277, h-index: 43)
Advances in Botanical Research     Full-text available via subscription   (Followers: 2, SJR: 0.619, h-index: 48)
Advances in Cancer Research     Full-text available via subscription   (Followers: 29, SJR: 2.215, h-index: 78)
Advances in Carbohydrate Chemistry and Biochemistry     Full-text available via subscription   (Followers: 7, SJR: 0.9, h-index: 30)
Advances in Catalysis     Full-text available via subscription   (Followers: 5, SJR: 2.139, h-index: 42)
Advances in Cell Aging and Gerontology     Full-text available via subscription   (Followers: 3)
Advances in Cellular and Molecular Biology of Membranes and Organelles     Full-text available via subscription   (Followers: 12)
Advances in Chemical Engineering     Full-text available via subscription   (Followers: 27, SJR: 0.183, h-index: 23)
Advances in Child Development and Behavior     Full-text available via subscription   (Followers: 10, SJR: 0.665, h-index: 29)
Advances in Chronic Kidney Disease     Full-text available via subscription   (Followers: 10, SJR: 1.268, h-index: 45)
Advances in Clinical Chemistry     Full-text available via subscription   (Followers: 28, SJR: 0.938, h-index: 33)
Advances in Colloid and Interface Science     Full-text available via subscription   (Followers: 19, SJR: 2.314, h-index: 130)
Advances in Computers     Full-text available via subscription   (Followers: 14, SJR: 0.223, h-index: 22)
Advances in Dermatology     Full-text available via subscription   (Followers: 15)
Advances in Developmental Biology     Full-text available via subscription   (Followers: 11)
Advances in Digestive Medicine     Open Access   (Followers: 8)
Advances in DNA Sequence-Specific Agents     Full-text available via subscription   (Followers: 5)
Advances in Drug Research     Full-text available via subscription   (Followers: 21)
Advances in Ecological Research     Full-text available via subscription   (Followers: 42, SJR: 3.25, h-index: 43)
Advances in Engineering Software     Hybrid Journal   (Followers: 27, SJR: 0.486, h-index: 10)
Advances in Experimental Biology     Full-text available via subscription   (Followers: 7)
Advances in Experimental Social Psychology     Full-text available via subscription   (Followers: 43, SJR: 5.465, h-index: 64)
Advances in Exploration Geophysics     Full-text available via subscription   (Followers: 1)
Advances in Fluorine Science     Full-text available via subscription   (Followers: 7)
Advances in Food and Nutrition Research     Full-text available via subscription   (Followers: 53, SJR: 0.674, h-index: 38)
Advances in Fuel Cells     Full-text available via subscription   (Followers: 15)
Advances in Genetics     Full-text available via subscription   (Followers: 15, SJR: 2.558, h-index: 54)
Advances in Genome Biology     Full-text available via subscription   (Followers: 8)
Advances in Geophysics     Full-text available via subscription   (Followers: 6, SJR: 2.325, h-index: 20)
Advances in Heat Transfer     Full-text available via subscription   (Followers: 21, SJR: 0.906, h-index: 24)
Advances in Heterocyclic Chemistry     Full-text available via subscription   (Followers: 9, SJR: 0.497, h-index: 31)
Advances in Human Factors/Ergonomics     Full-text available via subscription   (Followers: 22)
Advances in Imaging and Electron Physics     Full-text available via subscription   (Followers: 2, SJR: 0.396, h-index: 27)
Advances in Immunology     Full-text available via subscription   (Followers: 36, SJR: 4.152, h-index: 85)
Advances in Inorganic Chemistry     Full-text available via subscription   (Followers: 8, SJR: 1.132, h-index: 42)
Advances in Insect Physiology     Full-text available via subscription   (Followers: 2, SJR: 1.274, h-index: 27)
Advances in Integrative Medicine     Hybrid Journal   (Followers: 6)
Advances in Intl. Accounting     Full-text available via subscription   (Followers: 3)
Advances in Life Course Research     Hybrid Journal   (Followers: 8, SJR: 0.764, h-index: 15)
Advances in Lipobiology     Full-text available via subscription   (Followers: 1)
Advances in Magnetic and Optical Resonance     Full-text available via subscription   (Followers: 9)
Advances in Marine Biology     Full-text available via subscription   (Followers: 15, SJR: 1.645, h-index: 45)
Advances in Mathematics     Full-text available via subscription   (Followers: 11, SJR: 3.261, h-index: 65)
Advances in Medical Sciences     Hybrid Journal   (Followers: 6, SJR: 0.489, h-index: 25)
Advances in Medicinal Chemistry     Full-text available via subscription   (Followers: 5)
Advances in Microbial Physiology     Full-text available via subscription   (Followers: 4, SJR: 1.44, h-index: 51)
Advances in Molecular and Cell Biology     Full-text available via subscription   (Followers: 21)
Advances in Molecular and Cellular Endocrinology     Full-text available via subscription   (Followers: 8)
Advances in Molecular Toxicology     Full-text available via subscription   (Followers: 7, SJR: 0.324, h-index: 8)
Advances in Nanoporous Materials     Full-text available via subscription   (Followers: 3)
Advances in Oncobiology     Full-text available via subscription   (Followers: 1)
Advances in Organ Biology     Full-text available via subscription   (Followers: 1)
Advances in Organometallic Chemistry     Full-text available via subscription   (Followers: 15, SJR: 2.885, h-index: 45)
Advances in Parallel Computing     Full-text available via subscription   (Followers: 6, SJR: 0.148, h-index: 11)
Advances in Parasitology     Full-text available via subscription   (Followers: 5, SJR: 2.37, h-index: 73)
Advances in Pediatrics     Full-text available via subscription   (Followers: 24, SJR: 0.4, h-index: 28)
Advances in Pharmaceutical Sciences     Full-text available via subscription   (Followers: 10)
Advances in Pharmacology     Full-text available via subscription   (Followers: 15, SJR: 1.718, h-index: 58)
Advances in Physical Organic Chemistry     Full-text available via subscription   (Followers: 8, SJR: 0.384, h-index: 26)
Advances in Phytomedicine     Full-text available via subscription  
Advances in Planar Lipid Bilayers and Liposomes     Full-text available via subscription   (Followers: 3, SJR: 0.248, h-index: 11)
Advances in Plant Biochemistry and Molecular Biology     Full-text available via subscription   (Followers: 7)
Advances in Plant Pathology     Full-text available via subscription   (Followers: 5)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Protein Chemistry     Full-text available via subscription   (Followers: 17)
Advances in Protein Chemistry and Structural Biology     Full-text available via subscription   (Followers: 18, SJR: 1.5, h-index: 62)
Advances in Psychology     Full-text available via subscription   (Followers: 59)
Advances in Quantum Chemistry     Full-text available via subscription   (Followers: 6, SJR: 0.478, h-index: 32)
Advances in Radiation Oncology     Open Access  
Advances in Small Animal Medicine and Surgery     Hybrid Journal   (Followers: 3, SJR: 0.1, h-index: 2)
Advances in Space Biology and Medicine     Full-text available via subscription   (Followers: 5)
Advances in Space Research     Full-text available via subscription   (Followers: 385, SJR: 0.606, h-index: 65)
Advances in Structural Biology     Full-text available via subscription   (Followers: 5)
Advances in Surgery     Full-text available via subscription   (Followers: 9, SJR: 0.823, h-index: 27)
Advances in the Study of Behavior     Full-text available via subscription   (Followers: 29, SJR: 1.321, h-index: 56)
Advances in Veterinary Medicine     Full-text available via subscription   (Followers: 17)
Advances in Veterinary Science and Comparative Medicine     Full-text available via subscription   (Followers: 13)
Advances in Virus Research     Full-text available via subscription   (Followers: 5, SJR: 1.878, h-index: 68)
Advances in Water Resources     Hybrid Journal   (Followers: 46, SJR: 2.408, h-index: 94)
Aeolian Research     Hybrid Journal   (Followers: 6, SJR: 0.973, h-index: 22)
Aerospace Science and Technology     Hybrid Journal   (Followers: 337, SJR: 0.816, h-index: 49)
AEU - Intl. J. of Electronics and Communications     Hybrid Journal   (Followers: 8, SJR: 0.318, h-index: 36)
African J. of Emergency Medicine     Open Access   (Followers: 6, SJR: 0.344, h-index: 6)
Ageing Research Reviews     Hybrid Journal   (Followers: 10, SJR: 3.289, h-index: 78)
Aggression and Violent Behavior     Hybrid Journal   (Followers: 439, SJR: 1.385, h-index: 72)
Agri Gene     Hybrid Journal  
Agricultural and Forest Meteorology     Hybrid Journal   (Followers: 15, SJR: 2.18, h-index: 116)
Agricultural Systems     Hybrid Journal   (Followers: 31, SJR: 1.275, h-index: 74)
Agricultural Water Management     Hybrid Journal   (Followers: 43, SJR: 1.546, h-index: 79)
Agriculture and Agricultural Science Procedia     Open Access   (Followers: 1)
Agriculture and Natural Resources     Open Access   (Followers: 2)
Agriculture, Ecosystems & Environment     Hybrid Journal   (Followers: 56, SJR: 1.879, h-index: 120)
Ain Shams Engineering J.     Open Access   (Followers: 5, SJR: 0.434, h-index: 14)
Air Medical J.     Hybrid Journal   (Followers: 6, SJR: 0.234, h-index: 18)
AKCE Intl. J. of Graphs and Combinatorics     Open Access   (SJR: 0.285, h-index: 3)
Alcohol     Hybrid Journal   (Followers: 11, SJR: 0.922, h-index: 66)
Alcoholism and Drug Addiction     Open Access   (Followers: 9)
Alergologia Polska : Polish J. of Allergology     Full-text available via subscription   (Followers: 1)
Alexandria Engineering J.     Open Access   (Followers: 1, SJR: 0.436, h-index: 12)
Alexandria J. of Medicine     Open Access   (Followers: 1)
Algal Research     Partially Free   (Followers: 9, SJR: 2.05, h-index: 20)
Alkaloids: Chemical and Biological Perspectives     Full-text available via subscription   (Followers: 2)
Allergologia et Immunopathologia     Full-text available via subscription   (Followers: 1, SJR: 0.46, h-index: 29)
Allergology Intl.     Open Access   (Followers: 5, SJR: 0.776, h-index: 35)
Alpha Omegan     Full-text available via subscription   (SJR: 0.121, h-index: 9)
ALTER - European J. of Disability Research / Revue Européenne de Recherche sur le Handicap     Full-text available via subscription   (Followers: 9, SJR: 0.158, h-index: 9)
Alzheimer's & Dementia     Hybrid Journal   (Followers: 48, SJR: 4.289, h-index: 64)
Alzheimer's & Dementia: Diagnosis, Assessment & Disease Monitoring     Open Access   (Followers: 4)
Alzheimer's & Dementia: Translational Research & Clinical Interventions     Open Access   (Followers: 4)
Ambulatory Pediatrics     Hybrid Journal   (Followers: 6)
American Heart J.     Hybrid Journal   (Followers: 50, SJR: 3.157, h-index: 153)
American J. of Cardiology     Hybrid Journal   (Followers: 51, SJR: 2.063, h-index: 186)
American J. of Emergency Medicine     Hybrid Journal   (Followers: 44, SJR: 0.574, h-index: 65)
American J. of Geriatric Pharmacotherapy     Full-text available via subscription   (Followers: 10, SJR: 1.091, h-index: 45)
American J. of Geriatric Psychiatry     Hybrid Journal   (Followers: 14, SJR: 1.653, h-index: 93)
American J. of Human Genetics     Hybrid Journal   (Followers: 31, SJR: 8.769, h-index: 256)
American J. of Infection Control     Hybrid Journal   (Followers: 26, SJR: 1.259, h-index: 81)
American J. of Kidney Diseases     Hybrid Journal   (Followers: 34, SJR: 2.313, h-index: 172)
American J. of Medicine     Hybrid Journal   (Followers: 42, SJR: 2.023, h-index: 189)
American J. of Medicine Supplements     Full-text available via subscription   (Followers: 3)
American J. of Obstetrics and Gynecology     Hybrid Journal   (Followers: 197, SJR: 2.255, h-index: 171)
American J. of Ophthalmology     Hybrid Journal   (Followers: 62, SJR: 2.803, h-index: 148)
American J. of Ophthalmology Case Reports     Open Access   (Followers: 6)
American J. of Orthodontics and Dentofacial Orthopedics     Full-text available via subscription   (Followers: 6, SJR: 1.249, h-index: 88)
American J. of Otolaryngology     Hybrid Journal   (Followers: 25, SJR: 0.59, h-index: 45)
American J. of Pathology     Hybrid Journal   (Followers: 27, SJR: 2.653, h-index: 228)
American J. of Preventive Medicine     Hybrid Journal   (Followers: 27, SJR: 2.764, h-index: 154)
American J. of Surgery     Hybrid Journal   (Followers: 37, SJR: 1.286, h-index: 125)
American J. of the Medical Sciences     Hybrid Journal   (Followers: 12, SJR: 0.653, h-index: 70)
Ampersand : An Intl. J. of General and Applied Linguistics     Open Access   (Followers: 6)
Anaerobe     Hybrid Journal   (Followers: 4, SJR: 1.066, h-index: 51)
Anaesthesia & Intensive Care Medicine     Full-text available via subscription   (Followers: 62, SJR: 0.124, h-index: 9)
Anaesthesia Critical Care & Pain Medicine     Full-text available via subscription   (Followers: 14)
Anales de Cirugia Vascular     Full-text available via subscription  
Anales de Pediatría     Full-text available via subscription   (Followers: 3, SJR: 0.209, h-index: 27)
Anales de Pediatría (English Edition)     Full-text available via subscription  
Anales de Pediatría Continuada     Full-text available via subscription   (SJR: 0.104, h-index: 3)
Analytic Methods in Accident Research     Hybrid Journal   (Followers: 4, SJR: 2.577, h-index: 7)
Analytica Chimica Acta     Hybrid Journal   (Followers: 39, SJR: 1.548, h-index: 152)
Analytical Biochemistry     Hybrid Journal   (Followers: 170, SJR: 0.725, h-index: 154)
Analytical Chemistry Research     Open Access   (Followers: 10, SJR: 0.18, h-index: 2)
Analytical Spectroscopy Library     Full-text available via subscription   (Followers: 11)
Anesthésie & Réanimation     Full-text available via subscription   (Followers: 1)
Anesthesiology Clinics     Full-text available via subscription   (Followers: 22, SJR: 0.421, h-index: 40)
Angiología     Full-text available via subscription   (SJR: 0.124, h-index: 9)
Angiologia e Cirurgia Vascular     Open Access   (Followers: 1)

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Journal Cover Advances in Applied Mathematics
  [SJR: 1.054]   [H-I: 35]   [10 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0196-8858 - ISSN (Online) 1090-2074
   Published by Elsevier Homepage  [3175 journals]
  • Total positivity for the Lagrangian Grassmannian
    • Authors: Rachel Karpman
      Pages: 25 - 76
      Abstract: Publication date: July 2018
      Source:Advances in Applied Mathematics, Volume 98
      Author(s): Rachel Karpman
      The stratification of the Grassmannian by positroid varieties has been the subject of extensive research. Positroid varieties are in bijection with a number of combinatorial objects, including k-Bruhat intervals and bounded affine permutations. In addition, Postnikov's boundary measurement map gives a family of parametrizations of each positroid variety; the domain of each parametrization is the space of edge weights of a weighted planar network. In this paper, we generalize the combinatorics of positroid varieties to the Lagrangian Grassmannian Λ ( 2 n ) , which is the type C analog of the ordinary, or type A, Grassmannian. The Lagrangian Grassmannian has a stratification by projected Richardson varieties, which are the type C analogs of positroid varieties. We define type C generalizations of bounded affine permutations and k-Bruhat intervals, as well as several other combinatorial posets which index positroid varieties. In addition, we generalize Postnikov's network parametrizations to projected Richardson varieties in Λ ( 2 n ) . In particular, we show that restricting the edge weights of our networks to R + yields a family of parametrizations for totally nonnegative cells in Λ ( 2 n ) . In the process, we obtain a set of linear relations among the Plücker coordinates on Gr ( n , 2 n ) which cut out the Lagrangian Grassmannian set-theoretically.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.02.001
      Issue No: Vol. 98 (2018)
       
  • Phase transitions in stochastic non-linear threshold Boolean automata
           networks on Z2: The boundary impact
    • Authors: Jacques Demongeot; Sylvain Sené
      Pages: 77 - 99
      Abstract: Publication date: July 2018
      Source:Advances in Applied Mathematics, Volume 98
      Author(s): Jacques Demongeot, Sylvain Sené
      This paper addresses the question of the impact of the boundary on the dynamical behaviour of finite Boolean automata networks on Z2. The evolution over discrete time of such networks is governed by a specific stochastic threshold non-linear transition rule derived from the classical rule of formal neural networks. More precisely, the networks considered in this paper are finite but the study is done for arbitrarily large sizes. Moreover, the boundary impact is viewed as a classical definition of a phase transition in probability theory, characterising in our context the fact that a network admits distinct asymptotic behaviours when different boundary instances are assumed. The main contribution of this paper is the highlight of a formula for a necessary condition for boundary sensitivity, whose sufficiency and necessity are entirely proven with natural constraints on interaction potentials.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.03.003
      Issue No: Vol. 98 (2018)
       
  • Bumping sequences and multispecies juggling
    • Authors: Arvind Ayyer; Jérémie Bouttier; Sylvie Corteel; Svante Linusson; François Nunzi
      Pages: 100 - 126
      Abstract: Publication date: July 2018
      Source:Advances in Applied Mathematics, Volume 98
      Author(s): Arvind Ayyer, Jérémie Bouttier, Sylvie Corteel, Svante Linusson, François Nunzi
      Building on previous work by four of us (ABCN), we consider further generalizations of Warrington's juggling Markov chains. We first introduce “multispecies” juggling, which consist in having balls of different weights: when a ball is thrown it can possibly bump into a lighter ball that is then sent to a higher position, where it can in turn bump an even lighter ball, etc. We both study the case where the number of balls of each species is conserved and the case where the juggler sends back a ball of the species of its choice. In this latter case, we actually discuss three models: add-drop, annihilation and overwriting. The first two are generalisations of models presented in (ABCN) while the third one is new and its Markov chain has the ultra fast convergence property. We finally consider the case of several jugglers exchanging balls. In all models, we give explicit product formulas for the stationary probability and closed form expressions for the normalisation factor if known.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.03.001
      Issue No: Vol. 98 (2018)
       
  • A unifying combinatorial approach to refined little Göllnitz and
           Capparelli's companion identities
    • Authors: Shishuo Fu; Jiang Zeng
      Pages: 127 - 154
      Abstract: Publication date: July 2018
      Source:Advances in Applied Mathematics, Volume 98
      Author(s): Shishuo Fu, Jiang Zeng
      Berkovich–Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage–Sills's new little Göllnitz identities. Noticing the connection between their results and Boulet's earlier four-parameter partition generating functions, we discover a new class of partitions, called k-strict partitions, to generalize their results. By applying both horizontal and vertical dissections of Ferrers' diagrams with appropriate labellings, we provide a unified combinatorial treatment of their results and shed more lights on the intriguing conditions of their companion to Capparelli's identities.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.03.005
      Issue No: Vol. 98 (2018)
       
  • Signed countings of types B and D permutations and t,q-Euler numbers
    • Authors: Sen-Peng Eu; Tung-Shan Fu; Hsiang-Chun Hsu; Hsin-Chieh Liao
      Pages: 1 - 26
      Abstract: Publication date: June 2018
      Source:Advances in Applied Mathematics, Volume 97
      Author(s): Sen-Peng Eu, Tung-Shan Fu, Hsiang-Chun Hsu, Hsin-Chieh Liao
      It is a classical result that the parity-balance of the number of weak excedances of all permutations (derangements, respectively) of length n is the Euler number E n , alternating in sign, if n is odd (even, respectively). Josuat-Vergès obtained a q-analog of the results respecting the number of crossings of a permutation. One of the goals in this paper is to extend the results to the permutations (derangements, respectively) of types B and D, on the basis of the joint distribution in statistics excedances, crossings and the number of negative entries obtained by Corteel, Josuat-Vergès and Kim. Springer numbers are analogous Euler numbers that count the alternating permutations of type B, called snakes. Josuat-Vergès derived bivariate polynomials Q n ( t , q ) and R n ( t , q ) as generalized Euler numbers via successive q-derivatives and multiplications by t on polynomials in t. The other goal in this paper is to give a combinatorial interpretation of Q n ( t , q ) and R n ( t , q ) as the enumerators of the snakes with restrictions.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.02.004
      Issue No: Vol. 97 (2018)
       
  • Apéry sets of shifted numerical monoids
    • Authors: Christopher O'Neill; Roberto Pelayo
      Pages: 27 - 35
      Abstract: Publication date: June 2018
      Source:Advances in Applied Mathematics, Volume 97
      Author(s): Christopher O'Neill, Roberto Pelayo
      A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid S, consider the family of “shifted” monoids M n obtained by adding n to each generator of S. In this paper, we characterize the Apéry set of M n in terms of the Apéry set of the base monoid S when n is sufficiently large. We give a highly efficient algorithm for computing the Apéry set of M n in this case, and prove that several numerical monoid invariants, such as the genus and Frobenius number, are eventually quasipolynomial as a function of n.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.01.005
      Issue No: Vol. 97 (2018)
       
  • On the Andrews–Warnaar identities for partial theta functions
    • Authors: Jin Wang; Xinrong Ma
      Pages: 36 - 53
      Abstract: Publication date: June 2018
      Source:Advances in Applied Mathematics, Volume 97
      Author(s): Jin Wang, Xinrong Ma
      In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar but also unveils a new characteristic of such identities. As further applications, we establish a general form of Warnaar's identity and a general q-series transformation associated with Bailey pairs via the use of the power series expansion of partial theta functions.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.02.002
      Issue No: Vol. 97 (2018)
       
  • Refinements of two identities on (n,m)-Dyck paths
    • Authors: Rosena R.X. Du; Kuo Yu
      Pages: 54 - 63
      Abstract: Publication date: June 2018
      Source:Advances in Applied Mathematics, Volume 97
      Author(s): Rosena R.X. Du, Kuo Yu
      For integers n , m with n ≥ 1 and 0 ≤ m ≤ n , an ( n , m ) -Dyck path is a lattice path in the integer lattice Z × Z using up steps ( 0 , 1 ) and down steps ( 1 , 0 ) that goes from the origin ( 0 , 0 ) to the point ( n , n ) and contains exactly m up steps below the line y = x . The classical Chung–Feller theorem says that the total number of ( n , m ) -Dyck path is independent of m and is equal to the n-th Catalan number C n = 1 n + 1 ( 2 n n ) . For any integer k with 1 ≤ k ≤ n , let p n , m , k be the total number of ( n , m ) -Dyck paths with k peaks. Ma and Yeh proved that p n , m , k = p n , n − m , n − k for 0 ≤ m ≤ n , and p n , m , k + p n , m , n − k = p n , m + 1 , k + p n , m + 1 , n − k for 1 ≤ m ≤ n − 2 . In this paper we give bijective proofs of these two results. Using our bijections, we also get refined enumeration results on the numbers p n , m , k and p n , m , k + p n , m , n − k according to the starting and ending steps.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.01.006
      Issue No: Vol. 97 (2018)
       
  • Markov random fields and iterated toric fibre products
    • Authors: Jan Draisma; Florian M. Oosterhof
      Pages: 64 - 79
      Abstract: Publication date: June 2018
      Source:Advances in Applied Mathematics, Volume 97
      Author(s): Jan Draisma, Florian M. Oosterhof
      We prove that iterated toric fibre products from a finite collection of toric varieties are defined by binomials of uniformly bounded degree. This implies that Markov random fields built up from a finite collection of finite graphs have uniformly bounded Markov degree.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.02.003
      Issue No: Vol. 97 (2018)
       
  • Desingularization in the q-Weyl algebra
    • Authors: Christoph Koutschan; Yi Zhang
      Pages: 80 - 101
      Abstract: Publication date: June 2018
      Source:Advances in Applied Mathematics, Volume 97
      Author(s): Christoph Koutschan, Yi Zhang
      In this paper, we study the desingularization problem in the first q-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.02.005
      Issue No: Vol. 97 (2018)
       
  • On the powers of the descent set statistic
    • Authors: Richard Ehrenborg; Alex Happ
      Pages: 1 - 17
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Richard Ehrenborg, Alex Happ
      We study the sum of the rth powers of the descent set statistic and how many small prime factors occur in these numbers. Our results depend upon the base p expansion of n and r.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2017.10.003
      Issue No: Vol. 96 (2018)
       
  • Some useful theorems for asymptotic formulas and their applications to
           skew plane partitions and cylindric partitions
    • Authors: Guo-Niu Han; Huan Xiong
      Pages: 18 - 38
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Guo-Niu Han, Huan Xiong
      Inspired by the works of Dewar, Murty and Kotěšovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of skew plane partitions and cylindric partitions. We prove that the order of the asymptotic formula for the number of skew plane partitions of fixed width depends only on the width of the region, not on the profile (the skew zone) itself, while this is not true for cylindric partitions.

      PubDate: 2018-02-05T16:19:46Z
      DOI: 10.1016/j.aam.2017.12.007
      Issue No: Vol. 96 (2018)
       
  • Recovering a tree from the lengths of subtrees spanned by a randomly
           chosen sequence of leaves
    • Authors: Steven N. Evans; Daniel Lanoue
      Pages: 39 - 75
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Steven N. Evans, Daniel Lanoue
      Given an edge-weighted tree T with n leaves, sample the leaves uniformly at random without replacement and let W k , 2 ≤ k ≤ n , be the length of the subtree spanned by the first k leaves. We consider the question, “Can T be identified (up to isomorphism) by the joint probability distribution of the random vector ( W 2 , … , W n ) '” We show that if T is known a priori to belong to one of various families of edge-weighted trees, then the answer is, “Yes.” These families include the edge-weighted trees with edge-weights in general position, the ultrametric edge-weighted trees, and certain families with equal weights on all edges such as ( k + 1 ) -valent and rooted k-ary trees for k ≥ 2 and caterpillars.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.01.001
      Issue No: Vol. 96 (2018)
       
  • Minimal length maximal green sequences
    • Authors: Alexander Garver; Thomas McConville; Khrystyna Serhiyenko
      Pages: 76 - 138
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Alexander Garver, Thomas McConville, Khrystyna Serhiyenko
      Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the maximal green sequences of a quiver. We combine the combinatorics of surface triangulations and the basics of scattering diagrams to address this problem. Our main result is a formula for the length of minimal length maximal green sequences of quivers defined by triangulations of an annulus or a punctured disk.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2017.12.008
      Issue No: Vol. 96 (2018)
       
  • Almost balanced biased graph representations of frame matroids
    • Authors: Matt DeVos; Daryl Funk
      Pages: 139 - 175
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Matt DeVos, Daryl Funk
      Given a 3-connected biased graph Ω with a balancing vertex, and with frame matroid F ( Ω ) nongraphic and 3-connected, we determine all biased graphs Ω ′ with F ( Ω ′ ) = F ( Ω ) . As a consequence, we show that if M is a 4-connected nongraphic frame matroid represented by a biased graph Ω having a balancing vertex, then Ω essentially uniquely represents M. More precisely, all biased graphs representing M are obtained from Ω by replacing a subset of the edges incident to its unique balancing vertex with unbalanced loops.

      PubDate: 2018-02-05T16:19:46Z
      DOI: 10.1016/j.aam.2017.12.003
      Issue No: Vol. 96 (2018)
       
  • Warmth and edge spaces of graphs
    • Authors: Anton Dochtermann; Ragnar Freij-Hollanti
      Pages: 176 - 194
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Anton Dochtermann, Ragnar Freij-Hollanti
      In this paper we study a pair of numerical parameters associated to a graph G. On the one hand, we consider the (topological) connectivity of the polyhedral complex Hom ( K 2 , G ) , a space of homomorphisms from a edge K 2 into G. This approach dates back to the neighborhood complexes introduced by Lovász in his proof of the Kneser conjecture. In another direction we study the warmth ζ ( G ) of a graph G, a parameter introduced by Brightwell and Winkler based on the asymptotic behavior of d-branching walks in G and inspired by constructions in statistical physics. Both the warmth of G and the connectivity of Hom ( K 2 , G ) provide lower bounds on the chromatic number of G. Here we seek to relate these two constructions, and in particular we provide evidence for the conjecture that the warmth of a graph G is always less than three plus the connectivity of Hom ( K 2 , G ) . We succeed in establishing a first nontrivial case of the conjecture, by showing that ζ ( G ) ≤ 3 if Hom ( K 2 , G ) has an infinite first homology group. We also calculate warmth for a family of ‘twisted toroidal’ graphs that are important extremal examples in the context of Hom complexes. Finally we show that ζ ( G ) ≤ n − 1 if a graph G does not have the complete bipartite graph K a , b for a + b = n . This provides an analogue for a similar result in the context of Hom complexes.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2017.12.004
      Issue No: Vol. 96 (2018)
       
  • QRT maps and related Laurent systems
    • Authors: K. Hamad; A.N.W. Hone; P.H. van der Kamp; G.R.W. Quispel
      Pages: 216 - 248
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): K. Hamad, A.N.W. Hone, P.H. van der Kamp, G.R.W. Quispel
      In recent work it was shown how recursive factorisation of certain QRT maps leads to Somos-4 and Somos-5 recurrences with periodic coefficients, and to a fifth-order recurrence with the Laurent property. Here we recursively factorise the 12-parameter symmetric QRT map, given by a second-order recurrence, to obtain a system of three coupled recurrences which possesses the Laurent property. As degenerate special cases, we first derive systems of two coupled recurrences corresponding to the 5-parameter multiplicative and additive symmetric QRT maps. In all cases, the Laurent property is established using a generalisation of a result due to Hickerson, and exact formulae for degree growth are found from ultradiscrete (tropical) analogues of the recurrences. For the general 18-parameter QRT map it is shown that the components of the iterates can be written as a ratio of quantities that satisfy the same Somos-7 recurrence.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2017.12.006
      Issue No: Vol. 96 (2018)
       
  • Cyclically symmetric lozenge tilings of a hexagon with four holes
    • Authors: Tri Lai; Ranjan Rohatgi
      Pages: 249 - 285
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Tri Lai, Ranjan Rohatgi
      The work of Mills, Robbins, and Rumsey on cyclically symmetric plane partitions yields a simple product formula for the number of lozenge tilings of a regular hexagon, which are invariant under rotation by 120°. In this paper we generalize this result by enumerating the cyclically symmetric lozenge tilings of a hexagon in which four triangles have been removed in the center.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.aam.2018.01.003
      Issue No: Vol. 96 (2018)
       
  • Bowtie-free graphs have a Ramsey lift
    • Authors: Jan Hubička; Jaroslav Nešetřil
      Pages: 286 - 311
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Jan Hubička, Jaroslav Nešetřil
      A bowtie is a graph consisting of two triangles with one vertex identified. We show that the class of all (finite) graphs not containing a bowtie as a subgraph has a Ramsey lift (expansion). This solves one of the old problems in the area and it is the first Ramsey class with a non-trivial algebraic closure.

      PubDate: 2018-02-25T18:57:50Z
      DOI: 10.1016/j.aam.2017.12.005
      Issue No: Vol. 96 (2018)
       
  • 1324-avoiding permutations revisited
    • Authors: Andrew R. Conway; Anthony J. Guttmann; Paul Zinn-Justin
      Pages: 312 - 333
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Andrew R. Conway, Anthony J. Guttmann, Paul Zinn-Justin
      We give an improved algorithm for counting the number of 1324-avoiding permutations, resulting in 14 further terms of the generating function, which is now known for all lengths ≤50. We re-analyse the generating function and find additional evidence for our earlier conclusion that unlike other classical length-4 pattern-avoiding permutations, the generating function does not have a simple power-law singularity, but rather, the number of 1324-avoiding permutations of length n behaves as B ⋅ μ n ⋅ μ 1 n ⋅ n g . We estimate μ = 11.600 ± 0.003 , μ 1 = 0.0400 ± 0.0005 , g = − 1.1 ± 0.1 while the estimate of B depends sensitively on the precise value of μ, μ 1 and g. This reanalysis provides substantially more compelling arguments for the presence of the stretched exponential term μ 1 n .

      PubDate: 2018-02-25T18:57:50Z
      DOI: 10.1016/j.aam.2018.01.002
      Issue No: Vol. 96 (2018)
       
  • A Faà di Bruno subalgebra of the graded dual of word symmetric
           functions
    • Authors: Jean-Paul Bultel
      Pages: 334 - 359
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Jean-Paul Bultel
      We show that the graded dual of the Hopf algebra of word symmetric functions contains the Faà di Bruno algebra as a Hopf subalgebra. In this context, we give the expansion of natural generators of the Faà di Bruno algebra on a natural basis of this graded dual. We also give a combinatorial interpretation for the coefficients arising in this expansion.

      PubDate: 2018-02-25T18:57:50Z
      DOI: 10.1016/j.aam.2018.01.004
      Issue No: Vol. 96 (2018)
       
  • Hopf algebras and Tutte polynomials
    • Authors: Thomas Krajewski; Iain Moffatt; Adrian Tanasa
      Pages: 271 - 330
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Thomas Krajewski, Iain Moffatt, Adrian Tanasa
      By considering Tutte polynomials of Hopf algebras, we show how a Tutte polynomial can be canonically associated with combinatorial objects that have some notions of deletion and contraction. We show that several graph polynomials from the literature arise from this framework. These polynomials include the classical Tutte polynomial of graphs and matroids, Las Vergnas' Tutte polynomial of the morphism of matroids and his Tutte polynomial for embedded graphs, Bollobás and Riordan's ribbon graph polynomial, the Krushkal polynomial, and the Penrose polynomial. We show that our Tutte polynomials of Hopf algebras share common properties with the classical Tutte polynomial, including deletion-contraction definitions, universality properties, convolution formulas, and duality relations. New results for graph polynomials from the literature are then obtained as examples of the general results. Our results offer a framework for the study of the Tutte polynomial and its analogues in other settings, offering the means to determine the properties and connections between a wide class of polynomial invariants.

      PubDate: 2018-02-05T16:19:46Z
      DOI: 10.1016/j.aam.2017.12.001
      Issue No: Vol. 95 (2018)
       
  • Computation of all rational solutions of first-order algebraic ODEs
    • Authors: N. Thieu Vo; Georg Grasegger; Franz Winkler
      Pages: 127 - 139
      Abstract: Publication date: July 2018
      Source:Advances in Applied Mathematics, Volume 98
      Author(s): Thieu N. Vo, Georg Grasegger, Franz Winkler
      In this paper, we discuss three different approaches to attack the problem of determining all rational solutions for a first-order algebraic ordinary differential equation (AODE). We first give a sufficient condition for first-order AODEs to have the property that poles of rational solutions can only occur at the zeros of the leading coefficient. A combinatorial approach is presented to determine all rational solutions, if there are any, of the family of first-order AODEs satisfying this condition. Algebraic considerations based on algebraic function theory yield another algorithm for quasi-linear first-order AODEs. And finally ideas from algebraic geometry combine these results to an algorithm for finding all rational solutions of parametrizable first-order AODEs.

      PubDate: 2018-04-15T05:42:48Z
      DOI: 10.1016/j.jsc.2017.06.003
      Issue No: Vol. 87 (2018)
       
  • Bijective enumerations of Γ-free 0–1 matrices
    • Authors: Nagy
      Abstract: Publication date: May 2018
      Source:Advances in Applied Mathematics, Volume 96
      Author(s): Beáta Bényi, Gábor V. Nagy
      We construct a new bijection between the set of n × k 0–1 matrices with no three 1's forming a Γ configuration and the set of ( n , k ) -Callan sequences, a simple structure counted by poly-Bernoulli numbers. We give two applications of this result: We derive the generating function of Γ-free matrices, and we give a new bijective proof for an elegant result of Aval et al. that states that the number of complete non-ambiguous forests with n leaves is equal to the number of pairs of permutations of { 1 , … , n } with no common rise.

      PubDate: 2018-04-15T05:42:48Z
       
  • Small cells in a Poisson hyperplane tessellation
    • Authors: Gilles Bonnet
      Pages: 31 - 52
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Gilles Bonnet
      Until now, little was known about properties of small cells in a Poisson hyperplane tessellation. The few existing results were either heuristic or applying only to the two dimensional case and for very specific size functionals and directional distributions. This paper fills this gap by providing a systematic study of small cells in a Poisson hyperplane tessellation of arbitrary dimension, arbitrary directional distribution φ and with respect to an arbitrary size functional Σ. More precisely, we investigate the distribution of the typical cell Z, conditioned on the event { Σ ( Z ) < a } , where a → 0 and Σ is a size functional, i.e. a functional on the set of convex bodies which is continuous, not identically zero, homogeneous of degree k > 0 , and increasing with respect to set inclusion. We focus on the number of facets and the shape of such small cells. We show in various general settings that small cells tend to minimize the number of facets and that they have a non degenerated limit shape distribution which depends on the size Σ and the directional distribution. We also exhibit a class of directional distribution for which cells with small inradius do not tend to minimize the number of facets.

      PubDate: 2017-11-18T16:22:33Z
      DOI: 10.1016/j.aam.2017.11.002
      Issue No: Vol. 95 (2017)
       
  • Sturmian words and overexponential codimension growth
    • Authors: Antonio Giambruno; Mikhail Zaicev
      Pages: 53 - 64
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Antonio Giambruno, Mikhail Zaicev
      Let A be a non necessarily associative algebra over a field of characteristic zero satisfying a non-trivial polynomial identity. If A is a finite dimensional algebra or an associative algebra, it is known that the sequence c n ( A ) , n = 1 , 2 , … , of codimensions of A is exponentially bounded. If A is an infinite dimensional non associative algebra such sequence can have overexponential growth. Such phenomenon is present also in the case of Lie or Jordan algebras. In all known examples the smallest overexponential growth of c n ( A ) is ( n ! ) 1 2 . Here we construct a family of algebras whose codimension sequence grows like ( n ! ) α , for any real number α with 0 < α < 1 .

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.11.003
      Issue No: Vol. 95 (2017)
       
  • Neural ideals and stimulus space visualization
    • Authors: Elizabeth Gross; Nida Obatake; Nora Youngs
      Pages: 65 - 95
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Elizabeth Gross, Nida Obatake, Nora Youngs
      A neural code C is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from place cells, neurons that respond to geographic stimulus. In this setting, the stimulus space can be visualized as subset of R 2 covered by a collection U of convex sets such that the arrangement U forms an Euler diagram for C . There are some methods to determine whether such a convex realization U exists; however, these methods do not describe how to draw a realization. In this work, we look at the problem of algorithmically drawing Euler diagrams for neural codes using two polynomial ideals: the neural ideal, a pseudo-monomial ideal; and the neural toric ideal, a binomial ideal. In particular, we study how these objects are related to the theory of piercings in information visualization, and we show how minimal generating sets of the ideals reveal whether or not a code is 0, 1, or 2-inductively pierced.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.10.002
      Issue No: Vol. 95 (2017)
       
  • A minimaj-preserving crystal on ordered multiset partitions
    • Authors: Georgia Benkart; Laura Colmenarejo; Pamela E. Harris; Rosa Orellana; Greta Panova; Anne Schilling; Martha Yip
      Pages: 96 - 115
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Georgia Benkart, Laura Colmenarejo, Pamela E. Harris, Rosa Orellana, Greta Panova, Anne Schilling, Martha Yip
      We provide a crystal structure on the set of ordered multiset partitions, which recently arose in the pursuit of the Delta Conjecture. This conjecture was stated by Haglund, Remmel and Wilson as a generalization of the Shuffle Conjecture. Various statistics on ordered multiset partitions arise in the combinatorial analysis of the Delta Conjecture, one of them being the minimaj statistic, which is a variant of the major index statistic on words. Our crystal has the property that the minimaj statistic is constant on connected components of the crystal. In particular, this yields another proof of the Schur positivity of the graded Frobenius series of the generalization R n , k due to Haglund, Rhoades and Shimozono of the coinvariant algebra R n . The crystal structure also enables us to demonstrate the equidistributivity of the minimaj statistic with the major index statistic on ordered multiset partitions.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.11.006
      Issue No: Vol. 95 (2017)
       
  • Alternating sign matrices and hypermatrices, and a generalization of Latin
           squares
    • Authors: Richard A. Brualdi; Geir Dahl
      Pages: 116 - 151
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Richard A. Brualdi, Geir Dahl
      An alternating sign matrix, or ASM, is a ( 0 , ± 1 ) -matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an n × n × n hypermatrix A = [ a i j k ] is an alternating sign hypermatrix, or ASHM, if each of its planes, obtained by fixing one of the three indices, is an ASM. Several results concerning ASHMs are shown, such as finding the maximum number of nonzeros of an n × n × n ASHM, and properties related to Latin squares. Moreover, we investigate completion problems, in which one asks if a subhypermatrix can be completed (extended) into an ASHM. We show several theorems of this type.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.11.005
      Issue No: Vol. 95 (2017)
       
  • Selberg integral theory and Muttalib–Borodin ensembles
    • Authors: P.J. Forrester; J.R. Ipsen
      Pages: 152 - 176
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): P.J. Forrester, J.R. Ipsen
      We study Muttalib–Borodin ensembles — particular eigenvalue PDFs on the half-line — with classical weights, i.e. Laguerre, Jacobi or Jacobi prime. We show how the theory of the Selberg integral, involving also Jack and Schur polynomials, naturally leads to a multi-parameter generalisation of these particular Muttalib–Borodin ensembles, and also to the explicit form of underlying biorthogonal polynomials of a single variable. A suitable generalisation of the original definition of the Muttalib–Borodin ensemble allows for negative eigenvalues. In the cases of generalised Gaussian, symmetric Jacobi and Cauchy weights, we show that the problem of computing the normalisations and the biorthogonal polynomials can be reduced down to Muttalib–Borodin ensembles with classical weights on the positive half-line.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.11.004
      Issue No: Vol. 95 (2017)
       
  • A Poincaré series on hyperbolic space
    • Authors: Tathagata Basak
      Pages: 177 - 198
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Tathagata Basak
      Let L be the unique even self-dual lattice of signature ( 25 , 1 ) . The automorphism group Aut ( L ) acts on the hyperbolic space H 25 . We study a Poincaré series E ( z , s ) defined for z in H 25 , convergent for Re ( s ) > 25 , invariant under Aut ( L ) and having singularities along the mirrors of the reflection group of L. We compute the Fourier expansion of E ( z , s ) at a “Leech cusp” and prove that it can be meromorphically continued to Re ( s ) > 25 / 2 . Analytic continuation of Kloosterman sum zeta functions imply that the individual Fourier coefficients of E ( z , s ) have meromorphic continuation to the whole s-plane.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.10.004
      Issue No: Vol. 95 (2017)
       
  • Group actions on semimatroids
    • Authors: Emanuele Delucchi; Sonja Riedel
      Pages: 199 - 270
      Abstract: Publication date: April 2018
      Source:Advances in Applied Mathematics, Volume 95
      Author(s): Emanuele Delucchi, Sonja Riedel
      We initiate the study of group actions on (possibly infinite) semimatroids and geometric semilattices. To every such action is naturally associated an orbit-counting function, a two-variable “Tutte” polynomial and a poset which, in the representable case, coincides with the poset of connected components of intersections of the associated toric arrangement. In this structural framework we recover and strongly generalize many enumerative results about arithmetic matroids, arithmetic Tutte polynomials and toric arrangements by finding new combinatorial interpretations beyond the representable case. In particular, we thus find a class of natural examples of nonrepresentable arithmetic matroids. Moreover, we discuss actions that give rise to matroids over Z with natural combinatorial interpretations. As a stepping stone toward our results we also prove an extension of the cryptomorphism between semimatroids and geometric semilattices to the infinite case.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.11.001
      Issue No: Vol. 95 (2017)
       
  • A quasi-tree expansion of the Krushkal polynomial
    • Authors: Clark Butler
      Pages: 3 - 22
      Abstract: Publication date: March 2018
      Source:Advances in Applied Mathematics, Volume 94
      Author(s): Clark Butler
      We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the Bollobás–Riordan polynomial of a (possibly nonorientable) ribbon graph as a specialization. The quasi-tree expansion proven here then extends the recent quasi-tree expansions of the Bollobás–Riordan polynomial deduced in the oriented case by A. Champanerkar et al. and in the more general unoriented case by E. Dewey and F. Vignes-Tourneret. The generalized Krushkal polynomial also contains the Las Vergnas polynomial of a cellulation of a surface as a specialization; we use this fact to deduce a quasi-tree expansion for the Las Vergnas polynomial.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2016.06.003
      Issue No: Vol. 94 (2017)
       
  • A Tutte polynomial inequality for lattice path matroids
    • Authors: Kolja Knauer; Leonardo Martínez-Sandoval; Jorge Luis Ramírez Alfonsín
      Pages: 23 - 38
      Abstract: Publication date: March 2018
      Source:Advances in Applied Mathematics, Volume 94
      Author(s): Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín
      Let M be a matroid without loops or coloops and let T ( M ; x , y ) be its Tutte polynomial. In 1999 Merino and Welsh conjectured that max ⁡ ( T ( M ; 2 , 0 ) , T ( M ; 0 , 2 ) ) ≥ T ( M ; 1 , 1 ) holds for graphic matroids. Ten years later, Conde and Merino proposed a multiplicative version of the conjecture which implies the original one. In this paper we prove the multiplicative conjecture for the family of lattice path matroids (generalizing earlier results on uniform and Catalan matroids). In order to do this, we introduce and study particular lattice path matroids, called snakes, used as building bricks to indeed establish a strengthening of the multiplicative conjecture as well as a complete characterization of the cases in which equality holds.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2016.11.008
      Issue No: Vol. 94 (2017)
       
  • The G-invariant and catenary data of a matroid
    • Authors: Joseph E. Bonin; Joseph P.S. Kung
      Pages: 39 - 70
      Abstract: Publication date: March 2018
      Source:Advances in Applied Mathematics, Volume 94
      Author(s): Joseph E. Bonin, Joseph P.S. Kung
      The catenary data of a matroid M of rank r on n elements is the vector ( ν ( M ; a 0 , a 1 , … , a r ) ) , indexed by compositions ( a 0 , a 1 , … , a r ) , where a 0 ≥ 0 ,  a i > 0 for i ≥ 1 , and a 0 + a 1 + ⋯ + a r = n , with the coordinate ν ( M ; a 0 , a 1 , … , a r ) equal to the number of maximal chains or flags ( X 0 , X 1 , … , X r ) of flats or closed sets such that X i has rank i,  X 0 = a 0 , and X i − X i − 1 = a i . We show that the catenary data of M contains the same information about M as its G -invariant, which was defined by H. Derksen (2009) [9]. The Tutte polynomial is a specialization of the G -invariant. We show that many known results for the Tutte polynomial have analogs for the G -invariant. In particular, we show that for many matroid constructions, the G -invariant of the construction can be calculated from the G -invariants of the constituents and that the G -invariant of a matroid can be calculated from its size, the isomorphism class of the lattice of cyclic flats with lattice elements labeled by the rank and size of the underlying set. We also show that the number of flats and cyclic flats of a given rank and size can be derived from the G -invariant, that the G -invariant of M is reconstructible from the deck of G -invariants of restrictions of M to its copoints, and that, apart from free extensions and coextensions, one can detect whether a matroid is a free product from its G -invariant.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.03.001
      Issue No: Vol. 94 (2017)
       
  • On the complexity of generalized chromatic polynomials
    • Authors: A. Goodall; M. Hermann; T. Kotek; J.A. Makowsky; S.D. Noble
      Pages: 71 - 102
      Abstract: Publication date: March 2018
      Source:Advances in Applied Mathematics, Volume 94
      Author(s): A. Goodall, M. Hermann, T. Kotek, J.A. Makowsky, S.D. Noble
      J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings, called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for harmonious colorings, convex colorings, m c c t -colorings, and rainbow colorings, and many more. N. Linial (1986) showed that the chromatic polynomial χ ( G ; X ) is # P -hard to evaluate for all but three values X = 0 , 1 , 2 , where evaluation is in P. This dichotomy includes evaluation at real or complex values, and has the further property that the set of points for which evaluation is in P is finite. We investigate how the complexity of evaluating univariate graph polynomials that arise from CP-colorings varies for different evaluation points. We show that for some CP-colorings (harmonious, convex) the complexity of evaluation follows a similar pattern to the chromatic polynomial. However, in other cases (proper edge colorings, m c c t -colorings, H-free colorings) we could only obtain a dichotomy for evaluations at non-negative integer points. We also discuss some CP-colorings where we only have very partial results.

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.04.005
      Issue No: Vol. 94 (2017)
       
  • Partial graph orientations and the Tutte polynomial
    • Authors: Spencer Backman
      Pages: 103 - 119
      Abstract: Publication date: March 2018
      Source:Advances in Applied Mathematics, Volume 94
      Author(s): Spencer Backman
      Gessel and Sagan investigated the Tutte polynomial, T G ( x , y ) using depth-first search, and applied their techniques to show that the number of acyclic partial orientations of a graph is 2 m − n + 1 T G ( 3 , 1 / 2 ) . We provide a short deletion-contraction proof of this result and demonstrate that dually, the number of strongly connected partial orientations is 2 n − 1 T G ( 1 / 2 , 3 ) . We then prove that the number of partial orientations modulo cycle reversals is 2 g T G ( 3 , 1 ) and the number of partial orientations modulo cut reversals is 2 n − 1 T G ( 1 , 3 ) . To prove these results, we introduce cut and cycle-minimal partial orientations which provide distinguished representatives for partial orientations modulo cut and cycle reversals, extending known representatives for full orientations introduced by Greene and Zaslavksy. We then introduce distinguished partial orientations representing a given indegree sequence. We utilize these partial orientations to derive the Ehrhart polynomial of the win vector polytope, and give a combinatorial interpretation of its volume, thus answering a question of Bartels, Mount, and Welsh. We conclude with edge chromatic generalizations of the quantities presented, which allow for a new interpretation of the reliability polynomial for all probabilities p with 0 < p < 1 / 2 .

      PubDate: 2017-12-27T12:42:01Z
      DOI: 10.1016/j.aam.2017.05.003
      Issue No: Vol. 94 (2017)
       
  • k-divisible random variables in free probability
    • Authors: Octavio Arizmendi
      Pages: 1 - 68
      Abstract: Publication date: February 2018
      Source:Advances in Applied Mathematics, Volume 93
      Author(s): Octavio Arizmendi
      We introduce and study the notion of k-divisible elements in a non-commutative probability space. A k-divisible element is a (non-commutative) random variable whose n-th moment vanishes whenever n is not divisible by k. First, we consider the combinatorial convolution ⁎ in the lattices NC of non-crossing partitions and N C k of k-divisible non-crossing partitions and show that convolving k times with the zeta function in NC is equivalent to convolving once with the zeta function in N C k . Furthermore, when x is k-divisible, we derive a formula for the free cumulants of x k in terms of the free cumulants of x, involving k-divisible non-crossing partitions. Second, we prove that if a and s are free and s is k-divisible then sps and a are free, where p is any polynomial (on a and s) of degree k − 2 on s. Moreover, we define a notion of R-diagonal k-tuples and prove similar results. Next, we show that free multiplicative convolution between a measure concentrated in the positive real line and a probability measure with k-symmetry is well defined. Analytic tools to calculate this convolution are developed. Finally, we concentrate on free additive powers of k-symmetric distributions and prove that μ ⊞ t is a well defined k-symmetric probability measure, for all t > 1 . We derive central limit theorems and Poisson type ones. More generally, we consider freely infinitely divisible measures and prove that free infinite divisibility is maintained under the mapping μ → μ k . We conclude by focusing on (k-symmetric) free stable distributions, for which we prove a reproducing property generalizing the ones known for one sided and real symmetric free stable laws.

      PubDate: 2017-11-11T12:08:39Z
      DOI: 10.1016/j.aam.2017.09.001
      Issue No: Vol. 93 (2017)
       
  • Boundary measurement matrices for directed networks on surfaces
    • Authors: John Machacek
      Pages: 69 - 92
      Abstract: Publication date: February 2018
      Source:Advances in Applied Mathematics, Volume 93
      Author(s): John Machacek
      Franco, Galloni, Penante, and Wen have proposed a boundary measurement map for a graph on any closed orientable surface with boundary. We consider this boundary measurement map which takes as input an edge weighted directed graph embedded on a surface and produces on element of a Grassmannian. Computing the boundary measurement requires a choice of fundamental domain. Here the boundary measurement map is shown to be independent of the choice of fundamental domain Also, a formula for the Plücker coordinates of the element of the Grassmannian in the image of the boundary measurement map is given. The formula expresses the Plücker coordinates as a rational function which can be combinatorially described in terms of paths and cycles in the directed graph.

      PubDate: 2017-11-11T12:08:39Z
      DOI: 10.1016/j.aam.2017.09.002
      Issue No: Vol. 93 (2017)
       
  • New characterisations of tree-based networks and proximity measures
    • Authors: Andrew Francis; Charles Semple; Mike Steel
      Pages: 93 - 107
      Abstract: Publication date: February 2018
      Source:Advances in Applied Mathematics, Volume 93
      Author(s): Andrew Francis, Charles Semple, Mike Steel
      Phylogenetic networks are a type of directed acyclic graph that represent how a set X of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution, such networks are simply phylogenetic (evolutionary) trees. Moreover, phylogenetic networks that are not trees can sometimes be represented as phylogenetic trees with additional directed edges placed between their edges. Such networks are called tree-based, and the class of phylogenetic networks that are tree-based has recently been characterised. In this paper, we establish a number of new characterisations of tree-based networks in terms of path partitions and antichains (in the spirit of Dilworth's theorem), as well as via matchings in a bipartite graph. We also show that a temporal network is tree-based if and only if it satisfies an antichain-to-leaf condition. In the second part of the paper, we define three indices that measure the extent to which an arbitrary phylogenetic network deviates from being tree-based. We describe how these three indices can be computed efficiently using classical results concerning maximum-sized matchings in bipartite graphs.

      PubDate: 2017-11-11T12:08:39Z
      DOI: 10.1016/j.aam.2017.08.003
      Issue No: Vol. 93 (2017)
       
  • Preface: Special issue on the Tutte polynomial
    • Authors: Joanna A. Ellis Monaghan; Joseph P.S. Kung; Iain Moffatt
      Abstract: Publication date: Available online 6 October 2017
      Source:Advances in Applied Mathematics
      Author(s): Joanna A. Ellis Monaghan, Joseph P.S. Kung, Iain Moffatt


      PubDate: 2017-11-11T12:08:39Z
      DOI: 10.1016/j.aam.2017.09.005
       
  • Orienting transversals and transition polynomials of multimatroids
    • Authors: Robert Brijder
      Abstract: Publication date: Available online 22 July 2017
      Source:Advances in Applied Mathematics
      Author(s): Robert Brijder
      Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte–Martin polynomial. We prove evaluations of the Tutte–Martin polynomial of isotropic systems from Bouchet directly and more efficiently in the context of transition polynomials of multimatroids. Moreover, we generalize some related evaluations of the transition polynomial of 4-regular graphs from Jaeger to multimatroids. These evaluations are obtained in a uniform and matroid-theoretic way. We also translate the evaluations in terms of the interlace polynomial of graphs. Finally, we give an excluded-minor theorem for the class of binary tight 3-matroids (a subclass of multimatroids) based on the excluded-minor theorem for the class of binary delta-matroids from Bouchet.

      PubDate: 2017-07-23T04:06:40Z
      DOI: 10.1016/j.aam.2017.07.001
       
 
 
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