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: 3)
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: 39)
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: 5)
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: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 19)
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: 8)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
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: 2)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
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: 8)
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: 9)
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: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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)
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: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 11)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
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: 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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 7)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da 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: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
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: 2)
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  
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: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
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: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
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: 1)
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: 9)
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: 33)
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: 8)
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  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        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  [2469 journals]
  • The Number of Two-Term Tilting Complexes over Symmetric Algebras with
           Radical Cube Zero

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      Abstract: Abstract In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. First, we give a complete list of symmetric algebras with radical cube zero having only finitely many isomorphism classes of two-term tilting complexes in terms of their associated graphs. Secondly, we enumerate the number of two-term tilting complexes for each case in the list.
      PubDate: 2022-05-25
       
  • 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: 2022-05-16
       
  • Some More Identities of Kanade–Russell Type Derived Using
           Rosengren’s Method

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      Abstract: Abstract In the present paper, we consider some variations and generalizations of the multi-sum to single-sum transformation recently used by Rosengren in his proof of the Kanade–Russell identities. These general transformations are then used to prove a number of identities equating multi-sums and infinite products or multi-sums and infinite product \(\times \) a false theta series. Examples include the following: $$\begin{aligned}&\sum _{j,k,p,r=0}^{\infty } \frac{(-1)^{j+k} q^{ (2 j + k - p + r)^2/2 + k (k + 4)/2 + 3 j - p/2 + 3 r/2}(-q;q)_r}{\left( q^2;q^2\right) {}_j (q;q)_k (q;q)_p (q;q)_r} \\&\quad =2\frac{ \left( -q;q^2\right) {}_{\infty } \left( -q^2,-q^{14},q^{16};q^{16}\right) {}_{\infty }}{(q;q)_{\infty }}. \end{aligned}$$ Let $$\begin{aligned} Q(i,j,k,l,p):= & {} \frac{1}{2} (i+6j+4 k+2 l-p) (i+6 j+4 k+2 l-p-1)\\&+2 k (k-1)+l (l-1)+3 i +15j+14k+5 l-2 p. \end{aligned}$$ Then $$\begin{aligned}&\sum _{i,j,k,l,p=0}^{\infty } \frac{(-1)^{l+k}q^{Q(i,j,k,l,p)} }{ \left( q;q\right) {}_i \left( q^6;q^6\right) {}_j \left( q^4;q^4\right) {}_k \left( q^2;q^2\right) {}_l (q;q)_p } \\&\quad = \frac{2 (-q;q)_{\infty }^2 }{q \left( q^3;q^6\right) {}_{\infty } \left( q^4;q^4\right) {}_{\infty }}\left( 1+ \sum _{r=1}^{\infty } \left( q^{9 r^2+6 r}-q^{9 r^2-6 r}\right) \right) . \\&\sum _{j,k,p=0}^{\infty } (-1)^{k} \frac{q^{(3j+2k-p)(3j+2k-p-1)/2+k(k-1)-p+6j+6k} }{(q^3;q^3)_j(q^2;q^2)_{k} (q;q)_{p}}\\&\quad = \frac{ (-1;q)_{\infty }(q^{18};q^{18})_{\infty } }{ (q^3;q^3)_{\infty }(q^{9};q^{18})_{\infty } }. \end{aligned}$$
      PubDate: 2022-05-12
       
  • On the Universality and Extremality of Graphs with a Distance Constrained
           Colouring

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      Abstract: Abstract A lambda colouring (or L(2, 1)-colouring) of a graph is an assignment of non-negative integers (with minimum assignment 0) to its vertices such that the adjacent vertices must receive integers at least two apart and the vertices at distance two must receive distinct integers. The lambda chromatic number (or the \(\lambda \) number) of a graph G is the least non-negative integer among all the maximum assigned non-negative integer over all possible lambda colouring of the graph G. Here we have shown that every edge maximum graph with lambda chromatic number \(t\ge 5\) , admits an equitable L(2, 1) colouring. Further, we have established a classification result, identifying all possible n-vertex graphs with lambda chromatic number \(t\ge 3\) , where \(n\ge t+1\) , which contain the maximum number of edges. Such classification provides a complete solution to a problem posed more than two decades ago in 1996 by John P. Georges and David W. Mauro.
      PubDate: 2022-04-29
       
  • A Fast Algorithm for Computing the Number of Magic Series

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      Abstract: Abstract We present a fast algorithm for computing the number of magic series, an enumeration problem of a certain integer partition. Kinnaes showed that the number appears as a coefficient in a Gaussian polynomial and that the exact value can be efficiently extracted with a finite variant of Cauchy’s integral formula. The algorithm requires a bit time complexity of \(O(m^4 M(m \log m))\) and \(O(m \log m)\) -bit space, where m is the order of the magic series and \(M(n)\) is the time complexity of multiplying two n-bit numbers. Through our analysis, we confirm that this is the most efficient among previously reported algorithms. In addition, we show that the number can be computed with a bit time complexity of \(O(m^3 \log m M(m \log m))\) by directly carrying out polynomial multiplication and division on the Gaussian polynomial. Though the space consumption increases to \(O(m^3 \log m)\) bits, we demonstrate that our method actually computes the number faster for large orders.
      PubDate: 2022-04-28
       
  • Diamond Cone for $${{\mathfrak {sl}}}(m,n)$$ sl ( m , n )

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      Abstract: Abstract In this paper, we study the shape and the reduced shape algebra for the Lie superalgebra \({\mathfrak {sl}}(m,n)\) . We define quasistandard Young tableaux, and they give a combinatorial basis for the reduced shape algebra, called the diamond cone. There is a natural bijective map from the set of semistandard tableaux with shape \(\lambda \) to the set of quasistandard tableaux with smaller shape: the diamond cone is compatible with the stratification of the reduced shape algebra.
      PubDate: 2022-04-26
       
  • 3-Critical Subgraphs of Snarks

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      Abstract: Abstract In this paper we further our understanding of the structure of class two cubic graphs, or snarks, as they are commonly known. We do this by investigating their 3-critical subgraphs, or as we will call them, minimal conflicting subgraphs. We consider how the minimal conflicting subgraphs of a snark relate to its possible minimal 4-edge-colourings. We fully characterise the relationship between the resistance of a snark and the set of minimal conflicting subgraphs. That is, we show that the resistance of a snark is equal to the minimum number of edges which can be selected from the snark, such that the selection contains at least one edge from each minimal conflicting subgraph. We similarly characterise the relationship between what we call the critical subgraph of a snark and the set of minimal conflicting subgraphs. The critical subgraph being the set of all edges which are conflicting in some minimal colouring of the snark. Further to this, we define groups, or clusters, of minimal conflicting subgraphs. We then highlight some interesting properties and problems relating to clusters of minimal conflicting subgraphs.
      PubDate: 2022-04-26
       
  • Minimum Quantum Degrees for Isotropic Grassmannians in Types B and C

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      Abstract: Abstract We give a formula in terms of Young diagrams to calculate the minimum positive integer d such that \(q^d\) appears in the quantum product of two Schubert classes for the submaximal isotropic Grassmannians in types B and C. We do this by studying curve neighborhoods. We compute curve neighborhoods in several combinatorial models including k-strict partitions and a set of partitions where their inclusion is compatible with the Bruhat order.
      PubDate: 2022-04-22
       
  • Pattern Hopf Algebras

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      Abstract: Abstract In this paper, we expand on the notion of combinatorial presheaf, first introduced explicitly by Aguiar and Mahajan in 2010 but already present in the literature in some other points of view. We do this by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we consider functions that count the number of patterns of objects and endow the linear span of these functions with a product and a coproduct. In this way, any well-behaved family of combinatorial objects that admits a notion of substructure generates a Hopf algebra, and this association is functorial. For example, the Hopf algebra on permutations studied by Vargas in 2014 and the Hopf algebra on symmetric functions are particular cases of this construction. A specific family of pattern Hopf algebras of interest are the ones arising from commutative combinatorial presheaves. This includes the presheaves on graphs, posets and generalized permutahedra. Here, we show that all the pattern Hopf algebras corresponding to commutative presheaves are free. We also study a remarkable non-commutative presheaf structure on marked permutations, i.e. permutations with a marked element. These objects have a natural product called inflation, which is an operation motivated by factorization theorems for permutations. In this paper, we find new factorization theorems for marked permutations. We use these theorems to show that the pattern Hopf algebra for marked permutations is also free, using Lyndon words techniques.
      PubDate: 2022-04-19
       
  • Labeled Trees Generating Complete, Compact, and Discrete Ultrametric
           Spaces

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      Abstract: Abstract We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.
      PubDate: 2022-04-18
       
  • Permutations with Exactly One Copy of a Monotone Pattern of Length k, and
           a Generalization

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      Abstract: Abstract We construct an injection from the set of permutations of length n that contain exactly one copy of the decreasing pattern of length k to the set of permutations of length \(n+2\) that avoid that pattern. We then prove that the generating function counting the former is not rational, and in the case when k is even and \(k\ge 4\) , it is not even algebraic. We extend our injection and our nonrationality result to a larger class of patterns.
      PubDate: 2022-04-12
       
  • Polynomial Tau Functions of Symplectic KP and Multi-component Symplectic
           KP Hierarchies

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      Abstract: Abstract In this paper, we prove that a zero mode of an appropriate combinatorial generating function is a polynomial tau-function of a form of symplectic KP (SKP) hierarchy and extend it to the multi-component SKP hierarchy. Moreover, we write the polynomial tau-function of SKP hierarchy as determinant form in terms of the Vandermonde-like identity.
      PubDate: 2022-04-12
       
  • Matching in Power Graphs of Finite Groups

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      Abstract: Abstract The power graph P(G) of a finite group G is the undirected simple graph with vertex set G, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph \(P_e(G)\) of G (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of G.
      PubDate: 2022-03-13
      DOI: 10.1007/s00026-022-00576-5
       
  • Congruence Normality of Simplicial Hyperplane Arrangements via Oriented
           Matroids

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      Abstract: Abstract A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and also the weak order through the poset of regions. The weak order is known to be a congruence normal lattice, and congruence normality of lattices of regions of simplicial arrangements can be determined using polyhedral cones called shards. In this article, we update Grünbaum’s catalogue by providing normals realizing all known simplicial arrangements with up to 37 lines and key invariants. Then we add structure to this catalogue by determining which arrangements always/sometimes/never lead to congruence normal lattices of regions. To this end, we use oriented matroids to recast shards as covectors to determine congruence normality of large hyperplane arrangements. We also show that lattices of regions coming from finite Weyl groupoids of any rank are always congruence normal.
      PubDate: 2022-03-01
       
  • On a Theorem of Baxter and Zeilberger via a Result of Roselle

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      Abstract: Abstract We provide a new proof of a result of Baxter and Zeilberger showing that \({{\,\mathrm{inv}\,}}\) and \({{\,\mathrm{maj}\,}}\) on permutations are jointly independently asymptotically normally distributed. The main feature of our argument is that it uses a generating function due to Roselle, answering a question raised by Romik and Zeilberger.
      PubDate: 2022-02-11
      DOI: 10.1007/s00026-022-00570-x
       
  • ¿How do 9 Points Look Like in $$\mathbb {E}^3$$ E 3 '

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      Abstract: Abstract The aim of this note is to give an elementary proof of the following fact: given three red convex sets and three blue convex sets in \(\mathrm{I\!E}^3\) , such that every red intersects every blue, there is a line transversal to the reds or there is a line transversal to the blues. This is a special case of a theorem of Montajano and Karasev (Discrete Comput Geom 46(2):283–300, 2011) and generalizes, in a sense, the colourful Helly theorem due to Lovász (cf. Discrete Math 40(2,3):141–152, 1982)
      PubDate: 2022-01-30
      DOI: 10.1007/s00026-022-00568-5
       
  • On the Shifted Littlewood–Richardson Coefficients and the
           Littlewood–Richardson Coefficients

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      Abstract: Abstract We give a new interpretation of the shifted Littlewood–Richardson coefficients \(f_{\lambda \mu }^\nu \) ( \(\lambda ,\mu ,\nu \) are strict partitions). The coefficients \(g_{\lambda \mu }\) which appear in the decomposition of Schur Q-function \(Q_\lambda \) into the sum of Schur functions \(Q_\lambda = 2^{l(\lambda )}\sum \nolimits _{\mu }g_{\lambda \mu }s_\mu \) can be considered as a special case of \(f_{\lambda \mu }^\nu \) (here \(\lambda \) is a strict partition of length \(l(\lambda )\) ). We also give another description for \(g_{\lambda \mu }\) as the cardinal of a subset of a set that counts Littlewood–Richardson coefficients \(c_{\mu ^t\mu }^{{\tilde{\lambda }}}\) . This new point of view allows us to establish connections between \(g_{\lambda \mu }\) and \(c_{\mu ^t \mu }^{{\tilde{\lambda }}}\) . More precisely, we prove that \(g_{\lambda \mu }=g_{\lambda \mu ^t}\) , and \(g_{\lambda \mu } \le c_{\mu ^t\mu }^{{\tilde{\lambda }}}\) . We conjecture that \(g_{\lambda \mu }^2 \le c^{{\tilde{\lambda }}}_{\mu ^t\mu }\) and formulate some conjectures on our combinatorial models which would imply this inequality if it is valid.
      PubDate: 2022-01-24
      DOI: 10.1007/s00026-022-00566-7
       
  • Flexibility and Movability in Cayley Graphs

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      Abstract: Abstract Let \({\varvec{\Gamma }} = (V,E)\) be a (non-trivial) finite graph with \(\lambda : E \rightarrow {\mathbb {R}}_{+}\) an edge labeling of \({\varvec{\Gamma }}\) . Let \(\rho : V\rightarrow {\mathbb {R}}^{2}\) be a map which preserves the edge labeling, i.e., $$\begin{aligned} \Vert \rho (u) - \rho (v)\Vert _{2} = \lambda ((u,v)), \,\forall (u,v)\in E, \end{aligned}$$ where \(\Vert x-y\Vert _{2}\) denotes the Euclidean distance between two points \(x,y \in {\mathbb {R}}^{2}\) . The labeled graph is said to be flexible if there exists an infinite number of such maps (up to equivalence by rigid transformations) and it is said to be movable if there exists an infinite number of injective maps (again up to equivalence by rigid transformations). We study movability of Cayley graphs and construct regular movable graphs of all degrees. Further, we give explicit constructions of dense, movable graphs.
      PubDate: 2022-01-23
      DOI: 10.1007/s00026-022-00569-4
       
  • Positivity Among P-partition Generating Functions

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      Abstract: Abstract We seek simple conditions on a pair of labeled posets that determine when the difference of their \((P,\omega )\) -partition enumerators is F-positive, i.e., positive in Gessel’s fundamental basis. This is a quasisymmetric analogue of the extensively studied problem of finding conditions on a pair of skew shapes that determine when the difference of their skew Schur functions is Schur-positive. We determine necessary conditions and separate sufficient conditions for F-positivity, and show that a broad operation for combining posets preserves positivity properties. We conclude with classes of posets for which we have conditions that are both necessary and sufficient.
      PubDate: 2022-01-16
      DOI: 10.1007/s00026-021-00563-2
       
  • Complete Circular Regular Dessins of Type $$\{2^e,2^f\}$$ { 2 e , 2 f } I:
           Metacyclic Case

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      Abstract: Abstract A complete dessin of type \(\{2^e,2^f\}\) is an orientable map with underlying graph being a complete bipartite graph \(\mathbf{K}_{2^e,2^f}\) , which is said to be regular if all edges are equivalent under the group of color- and orientation-preserving automorphisms, and circular if the boundary cycle of each face is a circuit (a simple cycle). As one of a series papers towards a classification of complete circular regular dessins of type \(\{m,n\}\) , this paper presents such a classification for the case \(\{m,n\}=\{2^e,2^f\}\) , where e, f are positive integers and \(e\ge f\ge 2\) . We note that the group G of color- and orientation-preserving automorphisms is a bicyclic 2-group of type \(\{2^e,2^f\}\) , and our analysis splits naturally into two cases depending on whether the group G is metacyclic or not. In this paper, we deal with the case that G is metacyclic.
      PubDate: 2021-12-12
      DOI: 10.1007/s00026-021-00562-3
       
 
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