Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 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: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 43)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 20)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 21)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 6)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 15)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
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: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
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 Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
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  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 2)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
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: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 20)
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: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
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: 10)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
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  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     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: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0219-3094 - ISSN (Online) 0218-0006
Published by Springer-Verlag Homepage  [2467 journals]
  • Diameter Estimates for Graph Associahedra

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      Abstract: Abstract Graph associahedra are generalized permutohedra arising as special cases of nestohedra and hypergraphic polytopes. The graph associahedron of a graph G encodes the combinatorics of the search trees on G, defined recursively by a root r together with search trees on each of the connected components of \(G-r\) . In particular, the 1-skeleton of the corresponding graph associahedron is the rotation graph of those search trees. We investigate the diameter of graph associahedra as a function of some graph parameters. We give a tight bound of \(\Theta (m)\) on the diameter of trivially perfect graph associahedra on m edges. We consider the maximum diameter of associahedra of graphs on n vertices and of given tree-depth, treewidth, or pathwidth, and give lower and upper bounds as a function of these parameters. We also prove that the maximum diameter of associahedra of graphs of pathwidth two is \(\Theta (n\log n)\) . Finally, we give the exact diameter of the associahedra of complete split graphs and of unbalanced complete bipartite graphs.
      PubDate: 2022-12-01
       
  • File Placements, Fractional Matchings, and Normal Ordering

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      Abstract: Abstract In this paper, the bijection between k-rook placements on a Ferrers board and k-matchings in the associated bipartite graph is extended to a bijection between k-file placements and certain fractional matchings. Using the latter bijection, a new interpretation is given for the normal ordering coefficients in the shift algebra. Several further results concerning normal ordering in the shift algebra are derived.
      PubDate: 2022-12-01
       
  • Construction of Evidently Positive Series and an Alternative Construction
           for A Family of Partition Generating Functions Due to Kanade and Russell

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      Abstract: Abstract We give an alternative construction for a family of partition generating functions due to Kanade and Russell. In our alternative construction, we use ordinary partitions instead of jagged partitions. We also present new generating functions which are evidently positive series for partitions due to Kanade and Russell. To obtain those generating functions, we first construct an evidently positive series for a key infinite product. In that construction, a series of combinatorial moves is used to decompose an arbitrary partition into a base partition together with some auxiliary partitions that bijectively record the moves.
      PubDate: 2022-12-01
       
  • Pairwise Compatibility for 2-Simple Minded Collections II: Preprojective
           Algebras and Semibrick Pairs of Full Rank

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      Abstract: Abstract Let \(\Lambda \) be a finite-dimensional associative algebra over a field. A semibrick pair is a finite set of \(\Lambda \) -modules for which certain Hom- and Ext-sets vanish. A semibrick pair is completable if it can be enlarged so that a generating condition is satisfied. We prove that if \(\Lambda \) is \(\tau \) -tilting finite with at most three simple modules, then the completability of a semibrick pair can be characterized using conditions on pairs of modules. We then use the weak order to construct a combinatorial model for the semibrick pairs of preprojective algebras of type \(A_n\) . From this model, we deduce that any semibrick pair of size n satisfies the generating condition, and that the dimension vectors of any semibrick pair form a subset of the column vectors of some c-matrix. Finally, we show that no “pairwise” criteria for completability exists for preprojective algebras of Dynkin diagrams with more than three vertices.
      PubDate: 2022-12-01
       
  • Lozenge Tilings of a Hexagon with a Horizontal Intrusion

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      Abstract: Abstract Motivated by a conjecture posed by Fulmek and Krattenthaler, we provide product formulas for the number of lozenge tilings of a semiregular hexagon containing a horizontal intrusion. As a direct corollary, we obtain a product formula for the number of boxed plane partitions with a certain restriction. We also investigate the asymptotic behavior of the ratio between the number of lozenge tilings of a semiregular hexagon containing a horizontal intrusion and that of a semiregular hexagon without an intrusion.
      PubDate: 2022-12-01
       
  • Growing Random Uniform d-ary Trees

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      Abstract: Abstract Let \({{\mathcal {T}}}_{d}(n)\) be the set of d-ary rooted trees with n internal nodes. We give a method to construct a sequence \(( \textbf{t}_{n},n\ge 0)\) , where, for any \(n\ge 1\) , \( \textbf{t}_{n}\) has the uniform distribution in \({{\mathcal {T}}}_{d}(n)\) , and \( \textbf{t}_{n}\) is constructed from \( \textbf{t}_{n-1}\) by the addition of a new node, and a rearrangement of the structure of \( \textbf{t}_{n-1}\) . This method is inspired by Rémy’s algorithm which does this job in the binary case, but it is different from it. This provides a method for the random generation of a uniform d-ary tree in \({{\mathcal {T}}}_{d}(n)\) with a cost linear in n.
      PubDate: 2022-11-29
       
  • Large $$p$$ -Core $$p'$$ -Partitions and Walks on the Additive Residue
           Graph

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      Abstract: Abstract This paper investigates partitions which have neither parts nor hook lengths divisible by \(p\) , referred to as \(p\) -core \(p'\) -partitions. We show that the largest \(p\) -core \(p'\) -partition corresponds to the longest walk on a graph with vertices \(\{0, 1, \ldots , p-1\}\) and labelled edges defined via addition modulo \(p\) . We also exhibit an explicit family of large \(p\) -core \(p'\) -partitions, giving a lower bound on the size of the largest such partition which is of the same degree as the upper bound found by McSpirit and Ono.
      PubDate: 2022-11-24
       
  • The Limit Theorem with Respect to the Matrices on Non-backtracking
           Paths of a Graph

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      Abstract: Abstract We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the kth moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the \(p^m\) th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak.
      PubDate: 2022-11-15
       
  • Upper Bounds on the Smallest Positive Eigenvalue of Trees

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      Abstract: Abstract In this article, we undertake the problem of finding the first four trees on a fixed number of vertices with the maximum smallest positive eigenvalue. Let \({\mathcal {T}}_{n,d}\) denote the class of trees on n vertices with diameter d. First, we obtain the bounds on the smallest positive eigenvalue of trees in \({\mathcal {T}}_{n,d}\) for \(d =2,3,4\) and then upper bounds on the smallest positive eigenvalue of trees are obtained in general class of all trees on n vertices. Finally, the first four trees on n vertices with the maximum, second maximum, third maximum and fourth maximum smallest positive eigenvalue are characterized.
      PubDate: 2022-11-09
       
  • On Two-Sided Cayley Graphs of Semigroups and Groups

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      Abstract: Abstract In this paper, first we introduce the notion of two-sided Cayley graph of a semigroup. Then, we investigate some fundamental properties of these graphs and we use our results to give partial answers to some problems raised by Iradmusa and Praeger about two-sided group graphs (two-sided Cayley graphs of groups). Specially, as a consequence of our results, we determine all undirected two-sided Cayley graphs of groups which are connected. Furthermore, by introducing the notion of color-preserving automorphisms of a two-sided Cayley graph of a semigroup (group) and calculating them under some assumptions, we determine the family of color-vertex transitive two-sided Cayley graphs of semigroups (groups).
      PubDate: 2022-11-06
       
  • On Perfect Sequence Covering Arrays

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      Abstract: Abstract A PSCA \((v, t, \lambda )\) is a multiset of permutations of the v-element alphabet \(\{0, \dots , v-1\}\) , such that every sequence of t distinct elements of the alphabet appears in the specified order in exactly \(\lambda \) of the permutations. For \(v \geqslant t \geqslant 2\) , we define g(v, t) to be the smallest positive integer \(\lambda \) , such that a PSCA \((v, t, \lambda )\) exists. We show that \(g(6, 3) = g(7, 3) = g(7, 4) = 2\) and \(g(8, 3) = 3\) . Using suitable permutation representations of groups, we make improvements to the upper bounds on g(v, t) for many values of \(v \leqslant 32\) and \(3\leqslant t\leqslant 6\) . We also prove a number of restrictions on the distribution of symbols among the columns of a PSCA.
      PubDate: 2022-11-01
       
  • Asymptotics, Turán Inequalities, and the Distribution of the BG-Rank and
           2-Quotient Rank of Partitions

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      Abstract: Abstract Let j, n be even positive integers, and let \(\overline{p}_j(n)\) denote the number of partitions with BG-rank j, and \(\overline{p}_j(a,b;n)\) to be the number of partitions with BG-rank j and 2-quotient rank congruent to \(a \ \, \left( \mathrm {mod} \, b \right) \) . We give asymptotics for both statistics, and show that \(\overline{p}_j(a,b;n)\) is asymptotically equidistributed over the congruence classes modulo b. We also show that each of \(\overline{p}_j(n)\) and \(\overline{p}_j(a,b;n)\) asymptotically satisfy all higher-order Turán inequalities.
      PubDate: 2022-10-29
       
  • Sandpile Groups of Random Bipartite Graphs

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      Abstract: Abstract We determine the asymptotic distribution of the p-rank of the sandpile groups of random bipartite graphs. We see that this depends on the ratio between the number of vertices on each side, with a threshold when the ratio between the sides is equal to \(\frac{1}{p}\) . We follow the approach of Wood (J Am Math Soc 30(4):915–958, 2017) and consider random graphs as a special case of random matrices, and rely on a variant the definition of min-entropy given by Maples (Cokernels of random matrices satisfy the Cohen–Lenstra heuristics, 2013) to obtain useful results about these random matrices. Our results show that unlike the sandpile groups of Erdős–Rényi random graphs, the distribution of the sandpile groups of random bipartite graphs depends on the properties of the graph, rather than coming from some more general random group model.
      PubDate: 2022-10-29
       
  • Ramanujan’s Theta Functions and Parity of Parts and Cranks of
           Partitions

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      Abstract: Abstract In this paper, we explore intricate connections between Ramanujan’s theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation with the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.
      PubDate: 2022-10-25
       
  • A Proof of the $$\frac{n!}{2}$$ Conjecture for Hook Shapes

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      Abstract: Abstract A well-known representation-theoretic model for the transformed Macdonald polynomial \({\widetilde{H}}_\mu (Z;t,q)\) , where \(\mu \) is an integer partition, is given by the Garsia–Haiman module \({\mathcal {H}}_\mu \) . We study the \(\frac{n!}{k}\) conjecture of Bergeron and Garsia, which concerns the behavior of certain k-tuples of Garsia–Haiman modules under intersection. In the special case that \(\mu \) has hook shape, we use a basis for \({\mathcal {H}}_\mu \) due to Adin, Remmel, and Roichman to resolve the \(\frac{n!}{2}\) conjecture by constructing an explicit basis for the intersection of two Garsia–Haiman modules.
      PubDate: 2022-10-20
       
  • A Combinatorial Characterization of Cluster Algebras: On the Number of
           Arrows of Cluster Quivers

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      Abstract: Abstract Let \(\tilde{Q}\) (resp. Q) be an extended exchange (resp. exchange) cluster quiver of finite mutation type. We introduce the distribution set of the numbers of arrows for \(Mut[\tilde{Q}]\) (resp. Mut[Q]), give the maximum and minimum numbers of the distribution set and establish the existence of an extended complete walk (resp. a complete walk). As a consequence, we prove that the distribution set for \(Mut[\tilde{Q}]\) (resp. Mut[Q]) is continuous except in the case of exceptional cluster algebras. In case of cluster quivers \(Q_{inf}\) of infinite mutation type, the distribution set for \(Mut[Q_{inf}]\) in general is not continuous. Besides, we show that the maximal number of arrows of quivers in \(Mut[Q_{inf}]\) is infinite if and only if the maximal number of arrows between any two vertices of a quiver in \(Mut[Q_{inf}]\) is infinite.
      PubDate: 2022-10-06
       
  • Matching Complexes of Trees and Applications of the Matching Tree
           Algorithm

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      Abstract: Abstract A matching complex of a simple graph G is a simplicial complex with faces given by the matchings of G. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa showed that matching complexes of forests are contractible or homotopy equivalent to a wedge of spheres. We study two specific families of trees. For caterpillar graphs, we give explicit formulas for the number of spheres in each dimension and for perfect binary trees we find a strict connectivity bound. We also use a tool from discrete Morse theory called the Matching Tree Algorithm to study the connectivity of honeycomb graphs, partially answering a question raised by Jonsson.
      PubDate: 2022-09-27
       
  • The Free m-Cone of a Matroid and Its $${\mathcal {G}}$$ G -Invariant

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      Abstract: Abstract For a matroid, its configuration determines its \({\mathcal {G}}\) -invariant. Few examples are known of pairs of matroids with the same \({\mathcal {G}}\) -invariant but different configurations. In order to produce new examples, we introduce the free m-cone \(Q_m(M)\) of a loopless matroid M, where m is a positive integer. We show that the \({\mathcal {G}}\) -invariant of M determines the \({\mathcal {G}}\) -invariant of \(Q_m(M)\) , and that the configuration of \(Q_m(M)\) determines M; so if M and N are nonisomorphic and have the same \({\mathcal {G}}\) -invariant, then \(Q_m(M)\) and \(Q_m(N)\) have the same \({\mathcal {G}}\) -invariant but different configurations. We prove analogous results for several variants of the free m-cone. We also define a new matroid invariant of M, and show that it determines the Tutte polynomial of \(Q_m(M)\) .
      PubDate: 2022-09-13
      DOI: 10.1007/s00026-022-00606-2
       
  • Polycubes with Small Perimeter Defect

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      Abstract: Abstract In this paper, we consider enumeration of d-dimensional polycubes, whose perimeter (defined as the number of empty cells neighboring the polycube) has a fixed deviation from the maximum possible value. We provide a general framework for deriving such formulae, as well as several explicit formulae. In particular, we prove that for any fixed dimension d, the generating function that enumerates polycubes with a fixed defect (with respect to their volume) is rational. Moreover, its denominator is a product of cyclotomic polynomials.
      PubDate: 2022-09-10
      DOI: 10.1007/s00026-022-00601-7
       
  • Enumeration of Some Classes of Pattern Avoiding Matchings, with a Glimpse
           into the Matching Pattern Poset

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      Abstract: Abstract A matching of the set \([2n]=\{1,2,\ldots ,2n\}\) is a partition of [2n] into blocks with two elements, i.e. a graph on [2n], such that every vertex has degree one. Given two matchings \(\sigma \) and \(\tau \) , we say that \(\sigma \) is a \(pattern \) of \(\tau \) when \(\sigma \) can be obtained from \(\tau \) by deleting some of its edges and consistently relabelling the remaining vertices. This is a partial order relation turning the set of all matchings into a poset, which will be called the matching pattern poset. In this paper, we continue the study of classes of pattern avoiding matchings (see below for previous work on this subject). In particular, we work out explicit formulas to enumerate the class of matchings avoiding two new patterns, obtained by juxtaposition of smaller patterns, and we describe a recursive formula for the generating function of the class of matchings avoiding the lifting of a pattern and two additional patterns. Moreover, we introduce the notion of unlabeled pattern, as a combinatorial way to collect patterns, and we provide enumerative formulas for two classes of matchings avoiding an unlabeled pattern of order three. In one case, the enumeration follows from an interesting bijection between the matchings of the class and ternary trees. The last part of the paper initiates the study of the matching pattern poset, by providing some preliminary results about its Möbius functions and the structure of some simple intervals.
      PubDate: 2022-09-04
      DOI: 10.1007/s00026-022-00596-1
       
 
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