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  Subjects -> MATHEMATICS (Total: 966 journals)
    - APPLIED MATHEMATICS (82 journals)
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    - MATHEMATICS (711 journals)
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MATHEMATICS (711 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     Full-text available via subscription   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
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: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
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: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
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: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
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: 5)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (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: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, 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: 11)
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: 2)
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  
Annuaire du Collège de France     Open Access   (Followers: 5)
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: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
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: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
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)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
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: 12)
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: 1)
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: 4)
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 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  
Complexus     Full-text available via subscription  
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: 2)
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: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
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: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
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: 3)
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  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)

        1 2 3 4 | Last

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  [2350 journals]
  • Enumeration of Commuting Pairs in Lie Algebras over Finite Fields
    • Authors: Jason Fulman; Robert Guralnick
      Pages: 295 - 316
      Abstract: Feit and Fine derived a generating function for the number of ordered pairs of commuting \(n{\times}n\) matrices over the finite field \({\mathbb{F}_{q}}\) . This has been reproved and studied by Bryan and Morrison from the viewpoint of motivic Donaldson-Thomas theory. In this note, we give a new proof of the Feit-Fine result, and generalize it to the Lie algebra of finite unitary groups and to the Lie algebra of odd characteristic finite symplectic groups. We extract some asymptotic information from these generating functions. Finally, we derive generating functions for the number of commuting nilpotent elements for the Lie algebras of the finite general linear and unitary groups, and of odd characteristic symplectic groups.
      PubDate: 2018-06-01
      DOI: 10.1007/s00026-018-0390-4
      Issue No: Vol. 22, No. 2 (2018)
       
  • Two Murnaghan-Nakayama Rules in Schubert Calculus
    • Authors: Andrew Morrison; Frank Sottile
      Pages: 363 - 375
      Abstract: The Murnaghan-Nakayama rule expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. We establish a version of the Murnaghan- Nakayama rule for Schubert polynomials and a version for the quantum cohomology ring of the Grassmannian. These rules compute all intersections of Schubert cycles with tautological classes coming fromthe Chern character. Like the classical rule, both rules are multiplicity-free signed sums.
      PubDate: 2018-06-01
      DOI: 10.1007/s00026-018-0387-z
      Issue No: Vol. 22, No. 2 (2018)
       
  • From Partition Identities to a Combinatorial Approach to Explicit Satake
           Inversion
    • Abstract: In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands’ beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of \({{\rm Sym}^j}\) \({{{\rm Sym}^{k}}V}\) for \({{\rm GL}_2}\) in the case k = 3. We compute the plethysm explicitly for the cases k = 3, 4. Moreover, we use these expansions to explicitly compute the basic function attached to the symmetric power L-function of \({{\rm GL}_2}\) for these two cases.
      PubDate: 2018-06-06
      DOI: 10.1007/s00026-018-0391-3
       
  • Permutation Totally Symmetric Self-Complementary Plane Partitions
    • Abstract: Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permutations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations.
      PubDate: 2018-06-06
      DOI: 10.1007/s00026-018-0394-0
       
  • Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs
    • Authors: Ginji Hamano; Takayuki Hibi; Hidefumi Ohsugi
      Abstract: The fractional stable set polytope FRAC(G) of a simple graph G with d vertices is a rational polytope that is the set of nonnegative vectors (x1, . . . , x d ) satisfying x i +  xj \({\leq}\) 1 for every edge (i, j) of G. In this paper we show that (i) the \({\delta}\) -vector of a lattice polytope 2FRAC(G) is alternatingly increasing, (ii) the Ehrhart ring of FRAC(G) is Gorenstein, (iii) the coefficients of the numerator of the Ehrhart series of FRAC(G) are symmetric, unimodal and computed by the \({\delta}\) -vector of 2FRAC(G).
      PubDate: 2018-06-05
      DOI: 10.1007/s00026-018-0392-2
       
  • Once Punctured Disks, Non-Convex Polygons, and Pointihedra
    • Authors: Hugo Parlier; Lionel Pournin
      Abstract: We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once punctured polygons which, in turn, contain all possible geometric flip-graphs of polygons with a marked point as embedded sub-graphs. Our main focus is on the geometric properties of these graphs and how they relate to one another. In particular, we show that the embeddings between them are strongly convex (or, said otherwise, totally geodesic). We find bounds on the diameters of these graphs, sometimes using the strongly convex embeddings and show that the topological flip-graph is Hamiltonian. These graphs relate to different polytopes, namely to type D associahedra and a family of secondary polytopes which we call pointihedra.
      PubDate: 2018-06-05
      DOI: 10.1007/s00026-018-0393-1
       
  • Uniformly de Bruijn Sequences and Symbolic Diophantine Approximation on
           Fractals
    • Authors: Lior Fishman; Keith Merrill; David Simmons
      Abstract: Intrinsic Diophantine approximation on fractals, such as the Cantor ternary set, was undoubtedly motivated by questions asked by K. Mahler (1984). One of the main goals of this paper is to develop and utilize the theory of infinite de Bruijn sequences in order to answer closely related questions. In particular, we prove that the set of infinite de Bruijn sequences in \({k \geq 2}\) letters, thought of as a set of real numbers via a decimal expansion, has positive Hausdorff dimension. For a given k, these sequences bear a strong connection to Diophantine approximation on certain fractals. In particular, the optimality of an intrinsic Dirichlet function on these fractals with respect to the height function defined by symbolic representations of rationals follows from these results.
      PubDate: 2018-04-27
      DOI: 10.1007/s00026-018-0384-2
       
  • Hoste’s Conjecture and Roots of Link Polynomials
    • Authors: A. Stoimenow
      Abstract: In relation to a conjecture of Hoste on the roots of the Alexander polynomial of alternating knots, we prove that any root z of the Alexander polynomial of a 2-bridge (rational) knot or link satisfies \({ z^{1/2}-z^{-1/2} < 2}\) . We extend our result to properties of zeros for some Montesinos knots, and to an analogous statement about the skein polynomial. A similar estimate is derived for alternating 3-braid links.
      PubDate: 2018-04-27
      DOI: 10.1007/s00026-018-0389-x
       
  • AWilbrink-Like Equation for Neo-Difference Sets
    • Authors: Patrick G. Cesarz; Robert S. Coulter
      Abstract: Neo-difference sets arise in the study of projective planes of Lenz-Barlotti types I.3 and I.4. In the course of their proof that an abelian neo-difference set of order 3n satisfies either n = 1 or 3 n, Ghinelli and Jungnickel produce a Wilbrink-like equation for neo-difference sets of order 3n. In this note we generalise that part of their proof to produce a version of this equation that holds for all neo-difference sets.
      PubDate: 2018-04-23
      DOI: 10.1007/s00026-018-0382-4
       
  • An Algorithm to Prove Algebraic Relations Involving Eta Quotients
    • Authors: Cristian-Silviu Radu
      Abstract: In this paper, we present an algorithm which can prove algebraic relations involving \({\eta}\) -quotients, where \({\eta}\) is the Dedekind eta function.
      PubDate: 2018-04-23
      DOI: 10.1007/s00026-018-0388-y
       
  • Structure Constants for Immaculate Functions
    • Authors: Shu Xiao Li
      Abstract: The immaculate functions, \({\mathfrak{S}_a}\) , were introduced as a Schur-like basis for NSym, the ring of noncommutative symmetric functions. We investigate their structure constants. These are analogues of Littlewood-Richardson coefficents. We will give a new proof of the left Pieri rule for the \({\mathfrak{S}_a}\) , a translation invariance property for the structure coefficients of the \({\mathfrak{S}_a}\) , and a counterexample to an \({\mathfrak{S}_a}\) -analogue of the saturation conjecture.
      PubDate: 2018-04-23
      DOI: 10.1007/s00026-018-0386-0
       
  • Difference Operators for Partitions and Some Applications
    • Authors: Guo-Niu Han; Huan Xiong
      Abstract: Motivated by the Nekrasov-Okounkov formula on hook lengths, the first author conjectured that the Plancherel average of the 2k-th power sum of hook lengths of partitions with size n is always a polynomial of n for any \({k \in \mathbb{N}}\) . This conjecture was generalized and proved by Stanley (Ramanujan J. 23(1–3), 91–105 (2010)). In this paper, inspired by the work of Stanley and Olshanski on the differential poset of Young lattice, we study the properties of two kinds of difference operators D and \({D^{-}}\) defined on functions of partitions. Even though the calculations for higher orders of D are extremely complex, we prove that several wellknown families of functions of partitions are annihilated by a power of the difference operator D. As an application, our results lead to several generalizations of classic results on partitions, including the marked hook formula, Stanley Theorem, Okada-Panova hook length formula, and Fujii-Kanno-Moriyama-Okada content formula. We insist that the Okada constants K r arise directly from the computation for a single partition \({\lambda}\) , without the summation ranging over all partitions of size n.
      PubDate: 2018-04-23
      DOI: 10.1007/s00026-018-0385-1
       
  • On the Valuations of the Near Polygon $${\mathbb{H}_n}$$ H n
    • Authors: Bart De Bruyn
      Abstract: We characterize the valuations of the near polygon \({\mathbb{H}_n}\) that are induced by classical valuations of the dual polar space \({DW(2n-1, 2)}\) into which it is isometrically embeddable. An application to near 2n-gons that contain \({\mathbb{H}_n}\) as a full subgeometry is given.
      PubDate: 2018-04-23
      DOI: 10.1007/s00026-018-0383-3
       
  • Algebraic Independence of Sequences Generated by (Cyclotomic) Harmonic
           Sums
    • Authors: Jakob Ablinger; Carsten Schneider
      Abstract: Indefinite nested sums are important building blocks to assemble closed forms for combinatorial counting problems or for problems that arise, e.g., in particle physics. Concerning the simplicity of such formulas an important subtask is to decide if the arising sums satisfy algebraic relations among each other. Interesting enough, algebraic relations of such formal sums can be derived from combinatorial quasi-shuffle algebras. We will focus on the following question: can one find more relations if one evaluates these sums to sequences and looks for relations within the ring of sequences. In this article we consider the sequences of the rather general class of (cyclotomic) harmonic sums and show that their relations coincide with the relations found by their underlying quasi-shuffle algebra. In order to derive this result, we utilize the quasi-shuffle algebra and construct a difference ring with the following property: (1) the generators of the difference ring represent (cyclotomic) harmonic sums, (2) they generate within the ring all (cyclotomic) harmonic sums, and (3) the sequences produced by the generators are algebraically independent among each other. This means that their sequences do not satisfy any polynomial relations. The proof of this latter property is obtained by difference ring theory and new symbolic summation results. As a consequence, any sequence produced by (cyclotomic) harmonic sums can be formulated within our difference ring in an optimal way: there does not exist a subset of the arising sums in which the sequence can be formulated as polynomial expression.
      PubDate: 2018-04-23
      DOI: 10.1007/s00026-018-0381-5
       
  • A Classification of Orientably Edge-Transitive Circular Embeddings of
           $${{\rm K}_{{p^e}, p^{f}}}$$ K p e , p f
    • Authors: Wenwen Fan; Cai Heng Li; Hai Peng Qu
      Abstract: We show that a complete bipartite graph \({{\bf K}_{{p^e}, p_{f}}}\) , where p is an odd prime, has an edge-transitive embedding in an orientable surface with all faces bounded by simple cycles if and only if e = f. There are exactly \({p^{2(e-1)}}\) such embeddings up to isomorphism. Among them, \({p^{e-1}}\) are orientably regular, one of which is reflexible and \({p^{e-1} -1}\) form chiral pairs. The remaining \({p^{2(e-1)} - p^{e-1}}\) embeddings are non-regular (not arc-transitive). All of these embeddings have genus \({\frac{1}{2} (p^{e}-1) (p^{e}-2)}\) .
      PubDate: 2018-02-05
      DOI: 10.1007/s00026-018-0373-5
       
  • Remark on a Result of Constantine
    • Authors: Padraig Ó Catháin
      Abstract: In this short note we construct codes of length 4n with 8n+8 codewords and minimum distance 2n−2 whenever 4n+4 is the order of a Hadamard matrix. This generalises work of Constantine who obtained a similar result in the special case that n is a prime power.
      PubDate: 2018-02-05
      DOI: 10.1007/s00026-018-0379-z
       
  • Constructing Dominating Sets in Circulant Graphs
    • Authors: Igor E. Shparlinski
      Abstract: We give efficient constructions of reasonably small dominating sets of various types in a circulant graph on n notes and k distinct chord lengths. The structure of a cyclic group underlying circulant graph makes them suitable for applications of methods of analytic number theory. In particular, our results are based on bounds on some double exponential sums.
      PubDate: 2018-02-05
      DOI: 10.1007/s00026-018-0377-1
       
  • Universal Geometric Coefficients for the Four-Punctured Sphere
    • Authors: Emily Barnard; Emily Meehan; Nathan Reading; Shira Viel
      Abstract: We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the g-vectors of cluster variables. We also construct the rational part of the mutation fan. These constructions rely on a classification of the allowable curves (the curves which can appear in quasi-laminations). The classification allows us to prove the Null Tangle Property for the four-punctured sphere, thus adding this surface to a short list of surfaces for which this property is known. The Null Tangle Property then implies that the shear coordinates of allowable curves are the universal coefficients. We compute shear coordinates explicitly to obtain universal geometric coefficients.
      PubDate: 2018-02-05
      DOI: 10.1007/s00026-018-0378-0
       
  • Lattice Paths, Young Tableaux, and Weight Multiplicities
    • Authors: Rebecca L. Jayne; Kailash C. Misra
      Abstract: For \({\ell \geq 1}\) and \({k \geq 2}\) , we consider certain admissible sequences of k−1 lattice paths in a colored \({\ell \times \ell}\) square. We show that the number of such admissible sequences of lattice paths is given by the sum of squares of the number of standard Young tableaux of shape \({\lambda \vdash \ell}\) with \({l(\lambda) \leq k}\) , which is also the number of (k + 1)k··· 21-avoiding permutations in \({S_\ell}\) . Finally, we apply this result to the representation theory of the affine Lie algebra \({\widehat{sl}(n)}\) and show that this gives the multiplicity of certain maximal dominant weights in the irreducible highest weight \({\widehat{sl}(n)}\) -module \({V(k \Lambda_0)}\) .
      PubDate: 2018-02-02
      DOI: 10.1007/s00026-018-0374-4
       
  • Intersections of Maximal Subspaces of Zeros of Two Quadratic Forms
    • Authors: David B. Leep; Claus Schubert
      Abstract: We calculate the dimensions of the intersections of maximal subspaces of zeros of a nonsingular pair of quadratic forms. We then count the number of sets of distinct such subspaces that intersect in a given dimension.
      PubDate: 2018-02-01
      DOI: 10.1007/s00026-018-0375-3
       
 
 
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