A \(q\)-analogue for bi\(^{s}\)nomial coefficients and generalized Fibonacci sequences

DOI10.1016/j.crma.2014.01.009zbMath1294.11013OpenAlexW2018968482MaRDI QIDQ2445179

Hacène Belbachir, Athmane Benmezai

Publication date: 14 April 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2014.01.009

zbMATH Keywords

\(q\)-calculusFibonacci polynomialsbi\(^{s}\)nomial coefficients

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (13)

Log-concave sequences of bi\(^{\text{s}}\)nomial coefficients with their analogs and symmetric functions ⋮ Asymmetric extension of Pascal-Delannoy triangles ⋮ Unnamed Item ⋮ Two-Motzkin-like numbers and Stieltjes moment sequences ⋮ Overpartition analogues of \(q\text{-bi}^s\)nomial coefficients: basic properties and log-concavity ⋮ \(Q\)-total positivity and strong \(q\)-log-convexity for some generalized triangular arrays ⋮ On the self-convolution of generalized Fibonacci numbers ⋮ A \(q\)-analogue of the bi-periodic Fibonacci and Lucas sequences and Rogers-Ramanujan identities ⋮ Connection between bi s nomial coefficients and their analogs and symmetric functions ⋮ Preserving log-concavity for p,q-binomial coefficient ⋮ A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications ⋮ Congruence properties for \(\mathrm{bi}^s\)nomial coefficients and like extended Ram and Kummer theorems under suitable hypothesis ⋮ Unnamed Item

Cites Work

• An alternative approach to Cigler's \(q\)-Lucas polynomials
• Lattice gas generalization of the hard hexagon model. III: \(q\)-trinomial coefficients
• A new class of \(q\)-Fibonacci polynomials
• DETERMINING THE MODE FOR CONVOLUTION POWERS OF DISCRETE UNIFORM DISTRIBUTION
• Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution
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