The $q$-tangent and $q$-secant numbers via basic Eulerian polynomials

DOI10.1090/S0002-9939-09-10144-2zbMath1226.05023OpenAlexW1985906897WikidataQ56813885 ScholiaQ56813885MaRDI QIDQ5189162

Guo-Niu Han, Foata, Dominique

Publication date: 8 March 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-09-10144-2

zbMATH Keywords

excedancesderangementsalternating permutations\(q\)-secant numbers\(q\)-tangent numbers\(q\)-Eulerian polynomialsdesarrangements

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30)

Related Items (13)

Unnamed Item ⋮ Eulerian quasisymmetric functions ⋮ Eulerian polynomials, Stirling permutations of the second kind and perfect matchings ⋮ Hankel continued fractions and Hankel determinants of the Euler numbers ⋮ The \(q\)-Lidstone series involving \(q\)-Bernoulli and \(q\)-Euler polynomials generated by the third Jackson \(q\)-Bessel function ⋮ The \(\gamma\)-positivity of basic Eulerian polynomials via group actions ⋮ Signed countings of types B and D permutations and \(t,q\)-Euler numbers ⋮ Enumeration formulas for generalized \(q\)-Euler numbers ⋮ The \(q\)-tangent and \(q\)-secant numbers via continued fractions ⋮ A \(q\)-enumeration of alternating permutations ⋮ UNIMODALITY AND COLOURED HOOK FACTORISATION ⋮ q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials ⋮ Finite difference calculus for alternating permutations

Cites Work

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• Fix-Mahonian calculus. III: a quadruple distribution
• Congruences for the q-secant numbers
• Binomial posets, Möbius inversion, and permutation enumeration
• Another interpretation of the number of derangements
• 𝑞-Eulerian polynomials: Excedance number and major index
• Further Divisibility Properties of the q-Tangent Numbers
• A Coloring Problem
• A Combinatorial Property of q-Eulerian Numbers
• Divisibility Properties of the q-Tangent Numbers
• Permutations by Number of Rises and Successions
• q-Bernoulli and Eulerian Numbers

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