Search Results - "Exact enumeration problems, generating functions"

Periodicity and circulant matrices in the Riordan array of a polynomial

Authors: Nikolai A. Krylov

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

Subject Terms: 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

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

Conjugating cyclic \(n\)-color compositions

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

Source: Utilitas Mathematica. 122:53-64

Subject Terms: 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

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Noncommutative invariants of dihedral groups

Authors: Vesselin Drensky Boyan Kostadinov

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

Subject Terms: 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

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Access URL: http://arxiv.org/abs/2311.09380

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

Authors: Dousse, Jehanne Hardiman, Leonard Konan, Isaac

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

Subject Terms: 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

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Access 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

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

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

Subject Terms: 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)

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

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

Authors: Yusuke Nakamura

Source: Journal of Algebraic Combinatorics. 61

Subject Terms: 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

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Access URL: http://arxiv.org/abs/2408.10521

Bernoulli numbers with level 2

Authors: Komatsu, Takao

Source: Aequationes mathematicae. 99:71-87

Subject Terms: 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

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

On a Conjecture about Pattern Avoidance of Cyclic Permutations: On a conjecture about pattern avoidance of cyclic permutations

Authors: Junyao Pan

Source: Bulletin of the Malaysian Mathematical Sciences Society. 48

Subject Terms: Permutations, words, matrices, pattern avoidance, cyclic permutation, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Pell number

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Access URL: http://arxiv.org/abs/2409.17482

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

Authors: Deb, Bishal

Source: Combinatorial Theory, vol 5, iss 1

Subject Terms: 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

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Access 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

Authors: Mathilde Bouvel Rebecca Smith Jessica Striker

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

Subject Terms: 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.)

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

Shuffle series

Authors: Khushdil Ahmad Eric Rubiel Dolores-Cuenca Khurram Shabbir

Source: Journal of Algebraic Combinatorics. 61

Subject Terms: 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

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Access 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

Authors: Luis Ferroni Daniel McGinnis

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

Subject Terms: 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

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Access URL: http://arxiv.org/abs/2202.11808

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

Authors: FEIHU LIU

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

Subject Terms: 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

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Access URL: http://arxiv.org/abs/2312.10889

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

Authors: Sistos Barron, Jesus Omar Wang, Hua

Source: Combinatorial Number Theory ISBN: 9783111395593

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

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Access URL: https://zbmath.org/7860866

The Bernoulli clock: probabilistic and combinatorial interpretations of the Bernoulli polynomials by circular convolution

Authors: Yassine El Maazouz Jim Pitman

Source: Combinatorics, Probability and Computing. 33:210-237

Subject Terms: Permutations, words, matrices, Combinatorial probability, Bernoulli polynomials, Probability (math.PR), Exact enumeration problems, generating functions, 01 natural sciences, circular convolution, random permutations, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, Bernoulli clock, Mathematics - Probability

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Access URL: http://arxiv.org/abs/2210.02027
https://zbmath.org/7938722
https://doi.org/10.1017/s0963548323000421

Colored q-Stirling and q-Lah numbers: A new view continued: Colored \(q\)-Stirling and \(q\)-Lah numbers: a new view continued

Authors: Sen-Peng Eu Louis Kao Juei-Yin Lin

Source: Advances in Applied Mathematics. 168:102889

Subject Terms: Combinatorics of partially ordered sets, Lah numbers, topological interpretations, \(q\)-calculus and related topics, Exact enumeration problems, generating functions, \(q\)-analog, \(r\)-colored combinatorial structures, partially-ordered set, Stirling numbers

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A symmetry on weakly increasing trees and multiset Schett polynomials

Authors: Lin, Zhicong Ma, Jun

Source: Journal of Combinatorial Theory, Series A. 213:106010

Subject Terms: degrees or levels of nodes, Exact enumeration problems, generating functions, Sequences and sets, 0102 computer and information sciences, 01 natural sciences, increasing trees, Trees, Planar graphs, geometric and topological aspects of graph theory, plane trees, Elliptic functions and integrals, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, Jacobi elliptic functions

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Access URL: http://arxiv.org/abs/2104.10539
https://zbmath.org/8017442
https://doi.org/10.1016/j.jcta.2025.106010

On Stahl's conjectures about the region distributions of bouquets

Authors: Yichao Chen Zhicheng Gao

Source: Journal of Graph Theory. 109:201-209

Subject Terms: embedding, region distribution, median, Exact enumeration problems, generating functions, mode, 0102 computer and information sciences, 0101 mathematics, Enumeration in graph theory, Asymptotic enumeration, 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory

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

Authors: Zhonghua Li Lu Yan

Source: Advances in Applied Mathematics. 165:102853

Subject Terms: 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

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Access URL: http://arxiv.org/abs/2305.14031

On s-Stirling transform and poly-Cauchy numbers of the second kind with level 2: On \(s\)-Stirling transform and poly-Cauchy numbers of the second kind with level 2

Authors: Komatsu, Takao

Source: Aequationes mathematicae. 97:31-61

Subject Terms: poly-Cauchy numbers of the second kind, Other combinatorial number theory, Exact enumeration problems, generating functions, Bell and Stirling numbers, Stirling transform, Recurrences, Congruences, primitive roots, residue systems, 0102 computer and information sciences, 0101 mathematics, Bernoulli and Euler numbers and polynomials, 01 natural sciences, Combinatorial identities, bijective combinatorics, Stirling numbers

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Access URL: https://zbmath.org/7674007
https://doi.org/10.1007/s00010-022-00931-0