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  Subjects -> MATHEMATICS (Total: 1003 journals)
    - APPLIED MATHEMATICS (82 journals)
    - GEOMETRY AND TOPOLOGY (21 journals)
    - MATHEMATICS (742 journals)
    - MATHEMATICS (GENERAL) (41 journals)
    - NUMERICAL ANALYSIS (22 journals)
    - PROBABILITIES AND MATH STATISTICS (95 journals)

MATHEMATICS (742 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: 33)
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: 11)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 5)
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: 14)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 7)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Nonlinear Analysis     Hybrid Journal  
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: 13)
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     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: 10)
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  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
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: 3)
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: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 3)
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: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
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     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: 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: 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: 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 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  
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: 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: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
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: 13)
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

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  [2352 journals]
  • 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
       
  • Extremal Distances for Subtree Transfer Operations in Binary Trees
    • Authors: Ross Atkins; Colin McDiarmid
      Abstract: Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection (TBR), subtree prune and regraft (SPR), and rooted subtree prune and regraft (rSPR). We show that for a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is \(n-\Theta (\sqrt{n})\) , extending a result of Ding, Grünewald, and Humphries, and this holds also if one of the trees is fixed arbitrarily. If the pair is chosen uniformly at random, then the expected number of moves required is \(n-\Theta (n^{2/3})\) . These results may be phrased in terms of agreement forests: we also give extensions for more than two binary trees.
      PubDate: 2018-12-13
      DOI: 10.1007/s00026-018-0410-4
       
  • A Multidimensional Szemerédi Theorem in the Primes via Combinatorics
    • Authors: Brian Cook; Ákos Magyar; Tatchai Titichetrakun
      Abstract: Let A be a subset of positive relative upper density of \(\mathbb {P}^d\) , the d-tuples of primes. We present an essentially self-contained, combinatorial argument to show that A contains infinitely many affine copies of any finite set \(F\subseteq \mathbb {Z}^d\) . This provides a natural multidimensional extension of the theorem of Green and Tao on the existence of long arithmetic progressions in the primes.
      PubDate: 2018-11-30
      DOI: 10.1007/s00026-018-0402-4
       
  • Weyl Group $${\varvec{q}}$$ q -Kreweras Numbers and Cyclic Sieving
    • Authors: Victor Reiner; Eric Sommers
      Abstract: Catalan numbers are known to count noncrossing set partitions, while Narayana and Kreweras numbers refine this count according to the number of blocks in the set partition, and by its collection of block sizes. Motivated by reflection group generalizations of Catalan numbers and their q-analogues, this paper concerns a definition of q-Kreweras numbers for finite Weyl groups W, refining the q-Catalan numbers for W, and arising from work of the second author. We give explicit formulas in all types for the q-Kreweras numbers. In the classical types A, B, C, we also record formulas for the q-Narayana numbers and in the process show that the formulas depend only on the Weyl group (that is, they coincide in types B and C). In addition, we verify that in the classical types A, B, C, D the q-Kreweras numbers obey the expected cyclic sieving phenomena when evaluated at appropriate roots of unity.
      PubDate: 2018-11-13
      DOI: 10.1007/s00026-018-0408-y
       
  • Realization of Groups with Pairing as Jacobians of Finite Graphs
    • Authors: Louis Gaudet; David Jensen; Dhruv Ranganathan; Nicholas Wawrykow; Theodore Weisman
      Abstract: We study which groups with pairing can occur as the Jacobian of a finite graph. We provide explicit constructions of graphs whose Jacobian realizes a large fraction of odd groups with a given pairing. Conditional on the generalized Riemann hypothesis, these constructions yield all groups with pairing of odd order, and unconditionally, they yield all groups with pairing whose prime factors are sufficiently large. For groups with pairing of even order, we provide a partial answer to this question, for a certain restricted class of pairings. Finally, we explore which finite abelian groups occur as the Jacobian of a simple graph. There exist infinite families of finite abelian groups that do not occur as the Jacobians of simple graphs.
      PubDate: 2018-11-02
      DOI: 10.1007/s00026-018-0406-0
       
  • A Generalized SXP Rule Proved by Bijections and Involutions
    • Authors: Mark Wildon
      Abstract: This paper proves a combinatorial rule expressing the product \(s_\tau (s_{\lambda /\mu } \circ p_r)\) of a Schur function and the plethysm of a skew Schur function with a power-sum symmetric function as an integral linear combination of Schur functions. This generalizes the SXP rule for the plethysm \(s_\lambda \circ p_r\) . Each step in the proof uses either an explicit bijection or a sign-reversing involution. The proof is inspired by an earlier proof of the SXP rule due to Remmel and Shimozono (Discrete Math. 193:257–266, 1998). The connections with two later combinatorial rules for special cases of this plethysm are discussed. Two open problems are raised. The paper is intended to be readable by non-experts.
      PubDate: 2018-11-01
      DOI: 10.1007/s00026-018-0409-x
       
  • On the Crank Function of Cubic Partition Pairs
    • Authors: Byungchan Kim; Pee Choon Toh
      Abstract: We study a crank function M(m, n) for cubic partition pairs. We show that the function M(m, n) explains a cubic partition pair congruence and we also obtain various arithmetic properties regarding M(m, n). In particular, using the \(\Theta \) -operator, we confirm a conjecture on the sign pattern of c(n), the number of cubic partition pairs of n, weighted by the parity of the crank.
      PubDate: 2018-10-13
      DOI: 10.1007/s00026-018-0407-z
       
  • Prisms and Pyramids of Shelling Components
    • Authors: Richard Ehrenborg
      Abstract: We study how the shelling components behave under the pyramid and prism operations. As a consequence we obtain a concise recursion for the cubical shelling contributions.
      PubDate: 2018-10-11
      DOI: 10.1007/s00026-018-0412-2
       
  • Combinatorial Aspects of the Quantized Universal Enveloping Algebra of
           $$\mathfrak {sl}_{n+1}$$ sl n + 1
    • Authors: Raymond Cheng; David M. Jackson; Geoff J. Stanley
      Abstract: Quasi-triangular Hopf algebras were introduced by Drinfel’d in his construction of solutions to the Yang–Baxter Equation. This algebra is built upon \(\mathscr {U}_h(\mathfrak {sl}_2)\) , the quantized universal enveloping algebra of the Lie algebra \(\mathfrak {sl}_2\) . In this paper, combinatorial structure in \(\mathscr {U}_h(\mathfrak {sl}_2)\) is elicited, and used to assist in highly intricate calculations in this algebra. To this end, a combinatorial methodology is formulated for straightening algebraic expressions to a canonical form in the case \(n=1\) . We apply this formalism to the quasi-triangular Hopf algebras and obtain a constructive account not only for the derivation of the Drinfel’d’s \(sR\) -matrix, but also for the arguably mysterious ribbon elements of \(\mathscr {U}_h(\mathfrak {sl}_2)\) . Finally, we extend these techniques to the higher-dimensional algebras \(\mathscr {U}_h(\mathfrak {sl}_{n+1})\) . While these explicit algebraic results are well known, our contribution is in our formalism and perspective: our emphasis is on the combinatorial structure of these algebras and how that structure may guide algebraic constructions.
      PubDate: 2018-10-10
      DOI: 10.1007/s00026-018-0404-2
       
  • Permutations Resilient to Deletions
    • Authors: Noga Alon; Steve Butler; Ron Graham; Utkrisht C. Rajkumar
      Abstract: Let \(M = (s_1, s_2, \ldots , s_n) \) be a sequence of distinct symbols and \(\sigma \) a permutation of \(\{1,2, \ldots , n\}\) . Denote by \(\sigma (M)\) the permuted sequence \((s_{\sigma (1)}, s_{\sigma (2)}, \ldots , s_{\sigma (n)})\) . For a given positive integer d, we will say that \(\sigma \) is d-resilient if no matter how d entries of M are removed from M to form \(M'\) and d entries of \(\sigma (M)\) are removed from \(\sigma (M)\) to form \(\sigma (M)'\) (with no symbol being removed from both sequences), it is always possible to reconstruct the original sequence M from \(M'\) and \(\sigma (M)'\) . Necessary and sufficient conditions for a permutation to be d-resilient are established in terms of whether certain auxiliary graphs are acyclic. We show that for d-resilient permutations for [n] to exist, n must have size at least exponential in d, and we give an algorithm to construct such permutations in this case. We show that for each d and all sufficiently large n, the fraction of all permutations on n elements which are d-resilient is bounded away from 0.
      PubDate: 2018-10-05
      DOI: 10.1007/s00026-018-0403-3
       
  • Volume, Facets and Dual Polytopes of Twinned Chain Polytopes
    • Authors: Akiyoshi Tsuchiya
      Abstract: Let \((P,\le _P)\) and \((Q,\le _Q)\) be finite partially ordered sets with \( P = Q =d\) , and \(\mathcal {C}(P) \subset \mathbb {R}^d\) and \(\mathcal {C}(Q) \subset \mathbb {R}^d\) their chain polytopes. The twinned chain polytope of P and Q is the lattice polytope \(\Gamma (\mathcal {C}(P),\mathcal {C}(Q)) \subset \mathbb {R}^d\) which is the convex hull of \(\mathcal {C}(P) \cup (-\mathcal {C}(Q))\) . It is known that twinned chain polytopes are Gorenstein Fano polytopes with the integer decomposition property. In the present paper, we study combinatorial properties of twinned chain polytopes. First, we will give the formula of the volume of twinned chain polytopes in terms of the underlying partially ordered sets. Second, we will identify the facet-supporting hyperplanes of twinned chain polytopes in terms of the underlying partially ordered sets. Finally, we will provide the vertex representations of the dual polytopes of twinned chain polytopes.
      PubDate: 2018-10-05
      DOI: 10.1007/s00026-018-0405-1
       
  • The Distribution of the Carlitz Binomial Coefficients Modulo a Prime
    • Authors: Dong Quan Ngoc Nguyen
      Abstract: For a nonnegative integer n, and a prime \({\mathcal{P}}\) in \({\mathbb{F}_{q}[T]}\) , we prove a result that provides a method for computing the number of integers m with \({0 \leq m \leq n}\) for which the Carlitz binomial coefficients \({(_{m}^{n})_{C}}\) fall into each of the residue classes modulo \({\mathcal{P}}\) . Our main result can be viewed as a function field analogue of the Garfield-Wilf theorem.
      PubDate: 2018-07-27
      DOI: 10.1007/s00026-018-0400-6
       
  • Counting SET-Free Sets
    • Authors: Nate Harman
      Abstract: We consider the following counting problem related to the card game SET: how many k-element SET-free sets are there in an n-dimensional SET deck' Through a series of algebraic reformulations and reinterpretations, we show the answer to this question satisfies two polynomiality conditions.
      PubDate: 2018-07-27
      DOI: 10.1007/s00026-018-0401-5
       
  • On the Density of the Odd Values of the Partition Function
    • Authors: Samuel D. Judge; William J. Keith; Fabrizio Zanello
      Abstract: The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely, the conjecture that the partition function p(n) is equidistributed modulo 2. Our main result will relate the densities, say, \({\delta_t}\) , of the odd values of the t-multipartition functions \({p_t(n)}\) , for several integers t. In particular, we will show that if \({\delta_t > 0}\) for some \({t \in \{5, 7, 11, 13, 17, 19, 23, 25\}}\) , then (assuming it exists) \({\delta_1 > 0}\) ; that is, p(n) itself is odd with positive density. Notice that, currently, the best unconditional result does not even imply that p(n) is odd for \({\sqrt{x}}\) values of \({n \leq x}\) . In general, we conjecture that \({\delta_t = 1/2}\) for all t odd, i.e., that similarly to the case of p(n), all multipartition functions are in fact equidistributed modulo 2. Our arguments will employ a number of algebraic and analytic methods, ranging from an investigation modulo 2 of some classical Ramanujan identities and several other eta product results, to a unified approach that studies the parity of the Fourier coefficients of a broad class of modular form identities recently introduced by Radu.
      PubDate: 2018-07-24
      DOI: 10.1007/s00026-018-0397-x
       
  • Integer Partitions with Even Parts Below Odd Parts and the Mock Theta
           Functions
    • Authors: George E. Andrews
      Abstract: The paper begins with a study of a couple of classes of partitions in which each even part is smaller than each odd. In one class, a Dyson-type crank exists to explain a mod 5 congruence. The second part of the paper treats the arithmetic and combinatorial properties of the third order mock theta function \({\nu(q)}\) and relates the even part of \({\nu(q)}\) to the partitions initially considered. We also consider a surprisingly simple combinatorial relationship between the cranks and the ranks of the partition of n.
      PubDate: 2018-07-16
      DOI: 10.1007/s00026-018-0398-9
       
  • On Perturbations of Highly Connected Dyadic Matroids
    • Authors: Kevin Grace; Stefan H. M. van Zwam
      Abstract: Geelen, Gerards, and Whittle [3] announced the following result: let \({q = p^k}\) be a prime power, and let \({\mathcal{M}}\) be a proper minor-closed class of GF(q)-representable matroids, which does not contain PG(r − 1, p) for sufficiently high r. There exist integers k, t such that every vertically k-connected matroid in \({\mathcal{M}}\) is a rank- \({(\leq t)}\) perturbation of a frame matroid or the dual of a frame matroid over GF(q). They further announced a characterization of the perturbations through the introduction of subfield templates and frame templates. We show a family of dyadic matroids that form a counterexample to this result. We offer several weaker conjectures to replace the ones in [3], discuss consequences for some published papers, and discuss the impact of these new conjectures on the structure of frame templates.
      PubDate: 2018-07-16
      DOI: 10.1007/s00026-018-0396-y
       
  • Toric Degenerations of Gr(2, n ) and Gr(3, 6) via Plabic Graphs
    • Authors: L. Bossinger; X. Fang; G. Fourier; M. Hering; M. Lanini
      Abstract: We establish an explicit bijection between the toric degenerations of the Grassmannian Gr(2, n) arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to Gr(2, n). We show that a similar statement does not hold for Gr(3, 6).
      PubDate: 2018-07-16
      DOI: 10.1007/s00026-018-0395-z
       
  • 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
       
 
 
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