Connection between bi s nomial coefficients and their analogs and symmetric functions

DOI10.3906/mat-1705-27zbMath1424.05006OpenAlexW2802267010MaRDI QIDQ4634199

Moussa Ahmia, Abdelghafour Bazeniar, Hacène Belbachir

Publication date: 7 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1705-27

zbMATH Keywords

tilingsymmetric functionslattice pathsbi\(^{s}\)nomial coefficients

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Symmetric functions and generalizations (05E05)

Related Items (13)

Log-concave sequences of bi\(^{\text{s}}\)nomial coefficients with their analogs and symmetric functions ⋮ New modular symmetric function and its applications: modular \(s\)-Stirling numbers ⋮ Unnamed Item ⋮ Two-Motzkin-like numbers and Stieltjes moment sequences ⋮ Generalized Pascal's triangles and associated \(k\)-Padovan-like sequences ⋮ Overpartition analogues of \(q\text{-bi}^s\)nomial coefficients: basic properties and log-concavity ⋮ An analogue of Mahonian numbers and log-concavity ⋮ \(Q\)-total positivity and strong \(q\)-log-convexity for some generalized triangular arrays ⋮ s-Catalan numbers and Littlewood-Richardson polynomials ⋮ Preserving log-concavity for p,q-binomial coefficient ⋮ Congruence properties for \(\mathrm{bi}^s\)nomial coefficients and like extended Ram and Kummer theorems under suitable hypothesis ⋮ Unnamed Item ⋮ Petrie symmetric functions

Uses Software

• OEIS

Cites Work

• On the hyperbolic Pascal pyramid
• Hyperbolic Pascal triangles
• Lattice gas generalization of the hard hexagon model. III: \(q\)-trinomial coefficients
• A \(q\)-analogue for bi\(^{s}\)nomial coefficients and generalized Fibonacci sequences
• Subspaces, subsets, and partitions
• Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution
• Algebraic Combinatorics
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