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  Subjects -> MATHEMATICS (Total: 1014 journals)
    - APPLIED MATHEMATICS (82 journals)
    - GEOMETRY AND TOPOLOGY (21 journals)
    - MATHEMATICS (751 journals)
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    - NUMERICAL ANALYSIS (22 journals)
    - PROBABILITIES AND MATH STATISTICS (97 journals)

MATHEMATICS (751 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 35)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 13)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 6)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 11)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 7)
Advances in Pure Mathematics     Open Access   (Followers: 7)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 6)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 14)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access   (Followers: 1)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 8)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 7)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 2)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 14)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Educação Matemática Debate     Open Access  
EduMatSains     Open Access  
Electronic Journal of Combinatorics     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Annals of Combinatorics
Journal Prestige (SJR): 0.932
Citation Impact (citeScore): 1
Number of Followers: 4  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0219-3094 - ISSN (Online) 0218-0006
Published by Springer-Verlag Homepage  [2351 journals]
  • Abacus Proofs of Cauchy Product Identities for Schur Polynomials
    • Abstract: The well-known Cauchy Product Identities state that \(\prod _{i,j} (1-x_iy_j)^{-1}= \sum _{\lambda } s_{\lambda }(X) s_{\lambda }(Y)\) and \(\prod _{i,j} (1+x_iy_j)=\sum _{\lambda } s_{\lambda }(X)s_{\lambda '}(Y)\) , where \(s_{\lambda }\) denotes a Schur polynomial. The classical bijective proofs of these identities use the Robinson–Schensted–Knuth (RSK) algorithm to map matrices with entries in \({\mathbb {Z}}_{\ge 0}\) or \(\{0,1\}\) to pairs of semistandard tableaux. This paper gives new involution-based proofs of the Cauchy Product Identities using the abacus model for antisymmetrized Schur polynomials. These proofs provide a novel combinatorial perspective on these formulas in which carefully engineered sign cancellations gradually impose more and more structure on collections of matrices.
      PubDate: 2019-05-21
       
  • On the Zeros of a Class of Modular Functions
    • Abstract: We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose q-expansions satisfy the following: $$\begin{aligned} f_k(A; \tau )\, {:}{=}\,q^{-k}(1+a(1)q+a(2)q^2+\cdots ) + O(q), \end{aligned}$$ where a(n) are numbers satisfying a certain analytic condition. We show that the zeros of such \(f_k(\tau )\) in the fundamental domain of \(\text {SL}_2(\mathbb {Z})\) lie on \( \tau =1\) and are transcendental. We recover as a special case earlier work of Witten on extremal “partition” functions \(Z_k(\tau )\) . These functions were originally conceived as possible generalizations of constructions in three-dimensional quantum gravity.
      PubDate: 2019-05-20
       
  • Construction of Finite Braces
    • Abstract: Affine structures of a group G (=braces with adjoint group G) are characterized equationally without assuming further invertibility conditions. If G is finite, the construction of affine structures is reduced to affine structures of p, q-groups. The delicate relationship between finite solvable groups and involutive Yang–Baxter groups is further clarified by showing that much of an affine structure is already inherent in the Sylow system of the group. Semidirect products of braces are modified (shifted) in two ways to handle affine structures of semidirect products of groups. As an application, two of Vendramin’s conjectures on affine structures of p, q-groups are verified. A further example illustrates what happens beyond semidirect products.
      PubDate: 2019-05-17
       
  • Some Elementary Partition Inequalities and Their Implications
    • Abstract: We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for \(L\ge 1\) , the number of partitions with \(l-s \le L\) and \(s=1\) is greater than the number of partitions with \(l-s\le L\) and \(s>1\) . Here l and s are the largest part and the smallest part of the partition, respectively.
      PubDate: 2019-05-14
       
  • Properties of Non-symmetric Macdonald Polynomials at $$q=1$$ q = 1 and
           $$q=0$$ q = 0
    • Abstract: We examine the non-symmetric Macdonald polynomials \(\mathrm {E}_\lambda \) at \(q=1\) , as well as the more general permuted-basement Macdonald polynomials. When \(q=1\) , we show that \(\mathrm {E}_\lambda (\mathbf {x};1,t)\) is symmetric and independent of t whenever \(\lambda \) is a partition. Furthermore, we show that, in general \(\lambda \) , this expression factors into a symmetric and a non-symmetric part, where the symmetric part is independent of t, and the non-symmetric part only depends on \(\mathbf {x}\) , t, and the relative order of the entries in \(\lambda \) . We also examine the case \(q=0\) , which gives rise to the so-called permuted-basement t-atoms. We prove expansion properties of these t-atoms, and, as a corollary, prove that Demazure characters (key polynomials) expand positively into permuted-basement atoms. This complements the result that permuted-basement atoms are atom-positive. Finally, we show that the product of a permuted-basement atom and a Schur polynomial is again positive in the same permuted-basement atom basis. Haglund, Luoto, Mason, and van Willigenburg previously proved this property for the identity basement and the reverse identity basement, so our result can be seen as an interpolation (in the Bruhat order) between these two results. The common theme in this project is the application of basement-permuting operators as well as combinatorics on fillings, by applying results in a previous article by Per Alexandersson.
      PubDate: 2019-05-11
       
  • On the Relationship Between Ehrhart Unimodality and Ehrhart Positivity
    • Abstract: For a given lattice polytope, two fundamental problems within the field of Ehrhart theory are (1) to determine if its (Ehrhart) \(h^*\) -polynomial is unimodal and (2) to determine if its Ehrhart polynomial has only positive coefficients. The former property of a lattice polytope is known as Ehrhart unimodality and the latter property is known as Ehrhart positivity. These two properties are often simultaneously conjectured to hold for interesting families of lattice polytopes, yet they are typically studied in parallel. As to answer a question posed at the 2017 Introductory Workshop to the MSRI Semester on Geometric and Topological Combinatorics, the purpose of this note is to show that there is no general implication between these two properties in any dimension greater than two. To do so, we investigate these two properties for families of well-studied lattice polytopes, assessing one property where previously only the other had been considered. Consequently, new examples of each phenomena are developed, some of which provide an answer to an open problem in the literature. The well-studied families of lattice polytopes considered include zonotopes, matroid polytopes, simplices of weighted projective spaces, empty lattice simplices, smooth polytopes, and \({\varvec{s}}\) -lecture hall simplices.
      PubDate: 2019-05-10
       
  • Partitions and the Minimal Excludant
    • Abstract: Fraenkel and Peled have defined the minimal excludant or “ \({{\,\mathrm{mex}\,}}\) ” function on a set S of positive integers is the least positive integer not in S. For each integer partition \(\pi \) , we define \({{\,\mathrm{mex}\,}}(\pi )\) to be the least positive integer that is not a part of \(\pi \) . Define \(\sigma {{\,\mathrm{mex}\,}}(n)\) to be the sum of \({{\,\mathrm{mex}\,}}(\pi )\) taken over all partitions of n. It will be shown that \(\sigma {{\,\mathrm{mex}\,}}(n)\) is equal to the number of partitions of n into distinct parts with two colors. Finally the number of partitions \(\pi \) of n with \({{\,\mathrm{mex}\,}}(\pi )\) odd is almost always even.
      PubDate: 2019-05-03
       
  • A Proof of the Delta Conjecture When $$\varvec{q=0}$$ q = 0
    • Abstract: In Haglund et al. (Trans. Amer. Math. Soc. 370(6):4029–4057, 2018), Haglund, Remmel and Wilson introduce a conjecture which gives a combinatorial prediction for the result of applying a certain operator to an elementary symmetric function. This operator, defined in terms of its action on the modified Macdonald basis, has played a role in work of Garsia and Haiman on diagonal harmonics, the Hilbert scheme, and Macdonald polynomials (Garsia and Haiman in J. Algebraic Combin. 5:191–244, 1996; Haiman in Invent. Math. 149:371–407, 2002). The Delta Conjecture involves two parameters q, t; in this article we give the first proof that the Delta Conjecture is true when \(q=0\) or \(t=0\) .
      PubDate: 2019-05-03
       
  • Partitions with Parts Separated by Parity
    • Abstract: There have been a number of papers on partitions in which the parity of parts plays a central role. In this paper, the parts of partitions are separated by parity, either all odd parts are smaller than all even parts or vice versa. This concept first arose in a study related to the third-order mock theta function \(\nu (q)\) . The current study also leads back to one of the Ramanujan’s more mysterious functions.
      PubDate: 2019-05-02
       
  • Random Partitions and Cohen–Lenstra Heuristics
    • Abstract: We investigate combinatorial properties of a family of probability distributions on finite abelian p-groups. This family includes several well-known distributions as specializations. These specializations have been studied in the context of Cohen–Lenstra heuristics and cokernels of families of random p-adic matrices.
      PubDate: 2019-04-27
       
  • Representations of Weakly Multiplicative Arithmetic Matroids are Unique
    • Abstract: An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such an arithmetic matroid can be represented by an integer matrix, then this matrix is uniquely determined. This implies that the integral cohomology ring of a centered toric arrangement whose arithmetic matroid is weakly multiplicative is determined by its poset of layers. This partially answers a question asked by Callegaro–Delucchi.
      PubDate: 2019-04-26
       
  • Smooth Centrally Symmetric Polytopes in Dimension 3 are IDP
    • Abstract: In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda’s conjecture for centrally symmetric 3-dimensional polytopes, by showing they are covered by lattice parallelepipeds and unimodular simplices.
      PubDate: 2019-03-11
       
  • Two Families of Buffered Frobenius Representations of Overpartitions
    • Abstract: We generalize the generating series of the Dyson ranks and \(M_2\) -ranks of overpartitions to obtain k-fold variants and give a combinatorial interpretation of each. The k-fold generating series correspond to the full ranks of two families of buffered Frobenius representations, which generalize Lovejoy’s first and second Frobenius representations of overpartitions, respectively.
      PubDate: 2019-02-28
       
  • The Boustrophedon Transform for Descent Polytopes
    • Authors: Richard Ehrenborg; Alex Happ
      Abstract: We give a short proof that the f-vector of the descent polytope  \({{\,\mathrm{DP}\,}}_{\mathbf {v}}\) is componentwise maximized when the word \(\mathbf {v}\) is alternating. Our proof uses an f-vector analog of the boustrophedon transform.
      PubDate: 2019-02-12
      DOI: 10.1007/s00026-019-00422-1
       
  • Generalised Paley Graphs with a Product Structure
    • Authors: Geoffrey Pearce; Cheryl E. Praeger
      Abstract: A graph is Cartesian decomposable if it is isomorphic to a Cartesian product of strictly smaller graphs, each of which has more than one vertex and admits no such decomposition. These smaller graphs are called the Cartesian-prime factors of the Cartesian decomposition, and were shown, by Sabidussi and Vizing independently, to be uniquely determined up to isomorphism. We characterise by their parameters those generalised Paley graphs which are Cartesian decomposable, and we prove that for such graphs, the Cartesian-prime factors are themselves smaller generalised Paley graphs. This generalises a result of Lim and the second author which deals with the case where all the Cartesian-prime factors are complete graphs. These results contribute to the determination, by parameters, of generalised Paley graphs with automorphism groups larger than the one-dimensional affine subgroups used to define them. They also shed light on the structure of primitive cyclotomic association schemes.
      PubDate: 2019-02-10
      DOI: 10.1007/s00026-019-00423-0
       
  • Enumeration of Words that Contain the Pattern $$\varvec{123}$$ 123 Exactly
           Once
    • Authors: Mingjia Yang
      Abstract: Enumeration problems related to words avoiding patterns as well as permutations that contain the pattern 123 exactly once have been studied in great detail. However, the problem of enumerating words that contain the pattern 123 exactly once is new and will be the focus of this paper. Previously, Zeilberger provided a shortened version of Burstein’s combinatorial proof of Noonan’s theorem which states that the number of permutations with exactly one 321 pattern is equal to \(\frac{3}{n} \left( {\begin{array}{c}2n\\ n+3\end{array}}\right) \) . Surprisingly, a similar method can be directly adapted to words. We are able to use this method to find a formula enumerating the words with exactly one 123 pattern. Further inspired by Shar and Zeilberger’s work on generating functions enumerating 123-avoiding words with r occurrences of each letter, we examine the algebraic equations for generating functions for words with r occurrences of each letter and with exactly one 123 pattern.
      PubDate: 2019-02-08
      DOI: 10.1007/s00026-019-00416-z
       
  • Non-D-Finite Walks in a Three-Quadrant Cone
    • Authors: Sami Mustapha
      Abstract: We prove that the sequence \(\left( e_n^{\Gamma }\right) _{n\in \mathbb {N}}\) of numbers of excursions in a three-quadrant cone corresponding to a non-singular step set \(\Gamma \subset \{0, \pm 1\}^2\) with an infinite group does not satisfy any nontrivial linear recurrence with polynomial coefficients. This gives a positive answer to a question asked by M. Bousquet-Mélou about D-finiteness of the trivariate generating function of the numbers of walks with given length and prescribed ending point. In the process, we determine the asymptotics of \(e_n^{\Gamma }\) , \(n\rightarrow \infty \) , for the 74 non-singular two-dimensional models, giving the first complete computation of excursions asymptotics in a non-convex cone. Moreover, using potential theoretic comparison arguments, we give the asymptotics of the number of walks avoiding the negative quadrant and of length n for all non-singular step sets having zero drift.
      PubDate: 2019-02-06
      DOI: 10.1007/s00026-019-00413-2
       
  • Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields
           and Character Sums with Convolutions
    • Authors: Oliver Roche-Newton; Igor E. Shparlinski; Arne Winterhof
      Abstract: Balog and Wooley have recently proved that any subset \({\mathcal {A}}\) of either real numbers or of a prime finite field can be decomposed into two parts \({\mathcal {U}}\) and \({\mathcal {V}}\) , one of small additive energy and the other of small multiplicative energy. In the case of arbitrary finite fields, we obtain an analogue that under some natural restrictions for a rational function f both the additive energies of \({\mathcal {U}}\) and \(f({\mathcal {V}})\) are small. Our method is based on bounds of character sums which leads to the restriction \(\# {\mathcal {A}}> q^{1/2}\) , where q is the field size. The bound is optimal, up to logarithmic factors, when \(\# {\mathcal {A}}\ge q^{9/13}\) . Using \(f(X)=X^{-1}\) we apply this result to estimate some triple additive and multiplicative character sums involving three sets with convolutions \(ab+ac+bc\) with variables a, b, c running through three arbitrary subsets of a finite field.
      PubDate: 2019-02-02
      DOI: 10.1007/s00026-019-00420-3
       
  • Distribution of Descents in Matchings
    • Authors: Gene B. Kim
      Abstract: The distribution of descents in certain conjugacy classes of \(S_n\) has been previously studied, and it is shown that its moments have interesting properties. This paper provides a bijective proof of the symmetry of the descents and major indices of matchings (also known as fixed point free involutions) and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.
      PubDate: 2019-02-01
      DOI: 10.1007/s00026-019-00414-1
       
  • A High Quartet Distance Construction
    • Authors: Benny Chor; Péter L. Erdős; Yonatan Komornik
      Abstract: Given two binary trees on N labeled leaves, the quartet distance between the trees is the number of disagreeing quartets. By permuting the leaves at random, the expected quartet distance between the two trees is \(\frac{2}{3}\left( {\begin{array}{c}N\\ 4\end{array}}\right) \) . However, no strongly explicit construction reaching this bound asymptotically was known. We consider complete, balanced binary trees on \(N=2^n\) leaves, labeled by n bits long sequences. Ordering the leaves in one tree by the prefix order, and in the other tree by the suffix order, we show that the resulting quartet distance is \(\left( \frac{2}{3} + o(1)\right) \left( {\begin{array}{c}N\\ 4\end{array}}\right) \) , and it always exceeds the \(\frac{2}{3}\left( {\begin{array}{c}N\\ 4\end{array}}\right) \) bound.
      PubDate: 2019-01-05
      DOI: 10.1007/s00026-018-0411-3
       
 
 
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