Suchergebnisse - Exact enumeration problems, generating functions

GENERATING FUNCTIONS FOR THE QUOTIENTS OF NUMERICAL SEMIGROUPS: Generating functions for the quotients of numerical semigroups

Autoren: FEIHU LIU

Quelle: Bulletin of the Australian Mathematical Society. 110:427-438

Schlagwörter: quotient of a numerical semigroup, Exact enumeration problems, generating functions, 0102 computer and information sciences, systems of generators, 01 natural sciences, Arithmetic theory of semigroups, The Frobenius problem, FOS: Mathematics, Linear Diophantine equations, Sylvester denumerant, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, MacMahon's partition analysis

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2312.10889

Periodicity and circulant matrices in the Riordan array of a polynomial

Autoren: Nikolai A. Krylov

Quelle: Linear Algebra and its Applications. 718:58-80

Schlagwörter: Toeplitz, Cauchy, and related matrices, generating functions, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, 05A15, 15B05, Hermitian, skew-Hermitian, and related matrices, Combinatorics (math.CO), Riordan arrays, circulant matrices

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2308.02656
https://zbmath.org/8037032
https://doi.org/10.1016/j.laa.2025.04.005

Generating functions of multiple t-star values of general level: Generating functions of multiple \(t\)-star values of general level

Autoren: Zhonghua Li Lu Yan

Quelle: Advances in Applied Mathematics. 165:102853

Schlagwörter: 11M32, 05A15, generating function, Mathematics - Number Theory, Multiple Dirichlet series and zeta functions and multizeta values, Exact enumeration problems, generating functions, multiple \(t\)-star value, FOS: Mathematics, Number Theory (math.NT), alternating multiple \(t\)-half value, multiple \(t\)-star value of general level

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2305.14031

Conjugating cyclic \(n\)-color compositions

Autoren: Hopkins, Brian Barrón, Jesús Sistos Wang, Hua

Quelle: Utilitas Mathematica. 122:53-64

Schlagwörter: Combinatorial aspects of partitions of integers, combinatorial proofs, Exact enumeration problems, generating functions, \(n\)-color compositions, Elementary theory of partitions, integer compositions, Combinatorial identities, bijective combinatorics, cyclic compositions, conjugation

Dateibeschreibung: application/xml

Noncommutative invariants of dihedral groups

Autoren: Vesselin Drensky Boyan Kostadinov

Quelle: International Journal of Algebra and Computation. 35:343-355

Schlagwörter: Solvable, nilpotent (super)algebras, \(T\)-ideals, identities, varieties of associative rings and algebras, 16R10, 17B01, 05A15, 15A72, 16R40, 16W22, 17B30, 20D10, Identities, free Lie (super)algebras, Actions of groups and semigroups, invariant theory (associative rings and algebras), noncommutative invariant theory, Exact enumeration problems, generating functions, algebras with polynomial identity, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Identities other than those of matrices over commutative rings, Mathematics - Rings and Algebras, Group Theory (math.GR), free metabelian associative algebra, free metabelian Lie algebra, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Combinatorics, dihedral groups, Combinatorics (math.CO), Mathematics - Group Theory, Vector and tensor algebra, theory of invariants

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2311.09380

Partition identities from higher level crystals of 𝐴₁⁽¹⁾: Partition identities from higher level crystals of \(A_1^{(1)}\)

Autoren: Dousse, Jehanne Hardiman, Leonard Konan, Isaac

Quelle: Proceedings of the American Mathematical Society. 153:1363-1382

Schlagwörter: Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Exact enumeration problems, generating functions, Rogers-Ramanujan-type identities, 01 natural sciences, crystal bases, Partition identities, identities of Rogers-Ramanujan type, Mathematics - Quantum Algebra, FOS: Mathematics, Infinite-dimensional Lie (super)algebras, Mathematics - Combinatorics, Quantum Algebra (math.QA), Number Theory (math.NT), 0101 mathematics, Representation Theory (math.RT), Combinatorial identities, bijective combinatorics, Combinatorial aspects of partitions of integers, Mathematics - Number Theory, Elementary theory of partitions, character formulas, Kac-Moody (super)algebras, extended affine Lie algebras, toroidal Lie algebras, 05A15, 05A17, 05A30, 05E10, 11P81, 11P84, 17B10, 17B65, 17B67, Kac-Moody Lie algebras, integer partitions, Combinatorial aspects of representation theory, Combinatorics (math.CO), Mathematics - Representation Theory

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2111.10279
https://zbmath.org/7991239
https://doi.org/10.1090/proc/16417

Zeros of Hook Polynomials and Related Questions: Zeros of hook polynomials and related questions

Autoren: Bridges, Walter Craig, William Folsom, Amanda et al.

Quelle: Symmetry, Integrability and Geometry: Methods and Applications.

Schlagwörter: Combinatorial aspects of partitions of integers, zeros of polynomials, Mathematics - Number Theory, Exact enumeration problems, generating functions, theta functions, hook length, integer partitions, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), zero attractor, FOS: Mathematics, Mathematics - Combinatorics, Analytic theory of partitions, Theta series, Weil representation, theta correspondences, asymptotic behavior, Combinatorics (math.CO), Number Theory (math.NT)

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2408.16902
https://zbmath.org/8035728
https://doi.org/10.3842/sigma.2025.026

Bernoulli numbers with level 2

Autoren: Komatsu, Takao

Quelle: Aequationes mathematicae. 99:71-87

Schlagwörter: generating function, Other combinatorial number theory, Exact enumeration problems, generating functions, Bell and Stirling numbers, Recurrences, Bernoulli and Euler numbers and polynomials, Euler numbers, Combinatorial identities, bijective combinatorics, Bernoulli numbers

Dateibeschreibung: application/xml

Zugangs-URL: https://zbmath.org/8009173
https://doi.org/10.1007/s00010-024-01089-7

Exact enumeration of satisfiable 2-SAT formulae

Autoren: Dovgal, Sergey de Panafieu, Élie Ravelomanana, Vlady

Quelle: Combinatorial Theory. 3(2)

Schlagwörter: 2-CNF, exact enumeration, random graphs, phase transitions, strongly connected components, satisfiability, generating functions

Dateibeschreibung: application/pdf

Zugangs-URL: https://escholarship.org/uc/item/1m48c7s8
https://escholarship.org/content/qt1m48c7s8/qt1m48c7s8.pdf

Rationality of the multivariate growth series for algebraic sets of virtually abelian groups

Autoren: Yusuke Nakamura

Quelle: Journal of Algebraic Combinatorics. 61

Schlagwörter: Primary 20F65, Secondary 05A15, 05E16, virtually abelian group, growth series, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, periodic graph, Group Theory (math.GR), Combinatorics (math.CO), Geometric group theory, equations in groups, Mathematics - Group Theory, Combinatorial aspects of groups and algebras

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2408.10521

Generating functions for finite sums involving higher powers of binomial coefficients: Analysis of hypergeometric functions including new families of polynomials and numbers: Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers

Autoren: Yilmaz Simsek

Quelle: Journal of Mathematical Analysis and Applications. 477:1328-1352

Schlagwörter: Mathematics - Number Theory, Exact enumeration problems, generating functions, \(p\)-adic integrals, 01 natural sciences, Legendre polynomial, Classical hypergeometric functions, \({}_2F_1\), Franel numbers, generating functions, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Bernoulli and Euler numbers and polynomials, 11B83, 12D10, 11B68, 11S40, 11S80, 26C05, 26C10, 30B40, 30C15, Factorials, binomial coefficients, combinatorial functions, Mirimanoff polynomial

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/pdf/1901.02912
http://arxiv.org/abs/1901.02912
https://zbmath.org/7087671
https://doi.org/10.1016/j.jmaa.2019.05.015
https://arxiv.org/abs/1901.02912
https://ui.adsabs.harvard.edu/abs/2019arXiv190102912S/abstract
https://www.sciencedirect.com/science/article/pii/S0022247X19304032
https://arxiv.org/pdf/1901.02912
https://avesis.akdeniz.edu.tr/yayin/31eda6a0-c337-4d51-b7c3-cb7a28339f66/generating-functions-for-finite-sums-involving-higher-powers-of-binomial-coefficients-analysis-of-hypergeometric-functions-including-new-families-of-polynomials-and-numbers

Shuffle series

Autoren: Khushdil Ahmad Eric Rubiel Dolores-Cuenca Khurram Shabbir

Quelle: Journal of Algebraic Combinatorics. 61

Schlagwörter: Species, Hopf monoids, operads in combinatorics, operad, Hadamard product, 05A15 (Primary) 18M80, 05A10, 06A11, Exact enumeration problems, generating functions, shuffle, Algebraic aspects of posets, binomial, posets, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), series, Mathematics - Algebraic Topology, Combinatorics (math.CO), Factorials, binomial coefficients, combinatorial functions

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2311.08717
https://zbmath.org/8015153
https://doi.org/10.1007/s10801-025-01386-7

Lattice points in slices of prisms

Autoren: Luis Ferroni Daniel McGinnis

Quelle: Canadian Journal of Mathematics. 77:1013-1040

Schlagwörter: flag Eulerian numbers, Hilbert series, algebras of Veronese type, Exact enumeration problems, generating functions, hypersimplex, 0102 computer and information sciences, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Ehrhart polynomials, 01 natural sciences, Graded rings, 52B20, 05A15, 13D40, 13A02, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, Hilbert-Samuel and Hilbert-Kunz functions, Poincaré series

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2202.11808

On a problem of G. O. H. Katona

Autoren: Varecza, Á.

Quelle: Publicationes Mathematicae Debrecen. 37:165-174

Schlagwörter: Permutations, words, matrices, Exact enumeration problems, generating functions, comparisons, 0101 mathematics, problem of Katona, 01 natural sciences, finite ordered set

Dateibeschreibung: application/xml

Zugangs-URL: https://zbmath.org/9553

Balanced N-color compositions: Balanced \(n\)-color compositions

Autoren: Sistos Barron, Jesus Omar Wang, Hua

Quelle: Combinatorial Number Theory ISBN: 9783111395593

Schlagwörter: Permutations, words, matrices, regular compositions with restricted parts, Exact enumeration problems, generating functions, regular compositions with a centered maximum, Motzkin lattice paths, Mathematics

Dateibeschreibung: application/xml; application/pdf

Zugangs-URL: https://zbmath.org/7860866

Interlacing Property of a Family of Generating Polynomials over Dyck Paths: Interlacing property of a family of generating polynomials over Dyck paths

Autoren: Wang, Bo Zhang, Candice X. T.

Quelle: The Electronic Journal of Combinatorics. 31

Schlagwörter: Permutations, words, matrices, Combinatorics on words, Exact enumeration problems, generating functions, tantalizing symmetry on Catalan objects, 0102 computer and information sciences, Enumeration in graph theory, Sturm-unimodal sequence, 01 natural sciences, Real polynomials: location of zeros, Special sequences and polynomials, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2309.05903

Continued fractions using a Laguerre digraph interpretation of the Foata-Zeilberger bijection and its variants

Autoren: Deb, Bishal

Quelle: Combinatorial Theory, vol 5, iss 1

Schlagwörter: Permutations, words, matrices, Motzkin path, permutations, S-fraction, J-fraction, almost-Dyck path, Exact enumeration problems, generating functions, Permutations, T-fraction, continued fraction, 05A19 (Primary) 05A05, 05A10, 05A15, 05A30, 11B68, 30B70 (Secondary), Laguerre digraphs, Schröder path, \(q\)-calculus and related topics, FOS: Mathematics, Mathematics - Combinatorics, Dyck path, Combinatorics (math.CO), D-permutations, Foata-Zeilberger bijection, Bernoulli and Euler numbers and polynomials, Factorials, binomial coefficients, combinatorial functions, Combinatorial identities, bijective combinatorics, Continued fractions, complex-analytic aspects

Dateibeschreibung: application/xml; application/pdf

Zugangs-URL: http://arxiv.org/abs/2304.14487
https://zbmath.org/8017587
https://doi.org/10.5070/c65165020
https://escholarship.org/uc/item/35r6q8zv
https://escholarship.org/content/qt35r6q8zv/qt35r6q8zv.pdf

Key-avoidance for alternating sign matrices

Autoren: Mathilde Bouvel Rebecca Smith Jessica Striker

Quelle: Discrete Mathematics & Theoretical Computer Science, Vol vol. 27:1, Permutation..., Iss Special issues (2025)

Schlagwörter: Permutations, words, matrices, mathematics - combinatorics, 05A05, 05A19, Exact enumeration problems, generating functions, ASM key, alternating sign matrix, Matrices of integers, pattern avoidance, 05a05, 05a19, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Catalan numbers, permutation pattern, Mathematics, Combinatorial identities, bijective combinatorics, Combinatorial aspects of matrices (incidence, Hadamard, etc.)

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2408.05311
https://zbmath.org/8037131
https://doi.org/10.46298/dmtcs.14058
https://doaj.org/article/ace43f0360c14e85800f4b03f5874cb0

Generalization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices.

Autoren: Ostilli, M. Rocha, G. W. C. Bezerra, C. G. et al.

Quelle: Scientific Reports; 11/6/2024, Vol. 14 Issue 1, p1-7, 7p

Schlagwörter: GENERATING functions, PATH integrals, INTEGRAL functions, FERMIONS, GENERALIZATION

New Modular Symmetric Function and its Applications: Modular s-Stirling Numbers: New modular symmetric function and its applications: modular \(s\)-Stirling numbers

Autoren: Bazeniar Abdelghafour Moussa Ahmia José L. Ramírez et al.

Quelle: Bulletin of the Malaysian Mathematical Sciences Society. 45:1093-1109

Schlagwörter: Symmetric functions and generalizations, generating functions, Exact enumeration problems, generating functions, FOS: Mathematics, Bell and Stirling numbers, Mathematics - Combinatorics, symmetric functions, Combinatorics (math.CO), 05A15, 05A19, 0101 mathematics, 01 natural sciences, Combinatorial identities, bijective combinatorics, Stirling numbers

Dateibeschreibung: application/xml

Zugangs-URL: http://arxiv.org/abs/2110.10591
https://zbmath.org/7517461
https://doi.org/10.1007/s40840-022-01262-8