On the Eulerian polynomials of type \(D\).

DOI10.1016/S0195-6698(03)00027-1zbMath1033.05003arXivmath/0201140OpenAlexW1995441928MaRDI QIDQ1873774

Chak-On Chow

Publication date: 27 May 2003

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0201140

zbMATH Keywords

generating functionsCoxeter groupsrecurrence relationsdescentsEulerian polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Permutations, words, matrices (05A05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (11)

On certain combinatorial expansions of the Eulerian polynomials ⋮ On the descent numbers and major indices for the hyperoctahedral group ⋮ Recurrences for Eulerian polynomials of type B and type D ⋮ Enumeration by associated reflections on Coxeter systems ⋮ Enumeration of type \(D\) permutations with alternating runs ⋮ An asymptotic distribution theory for Eulerian recurrences with applications ⋮ Strong \(q\)-log-convexity of the Eulerian polynomials of Coxeter groups ⋮ Enumerating \(S_n\) by associated transpositions and linear extensions of finite posets ⋮ New proofs of interlacing of zeros of Eulerian polynomials ⋮ Signed words and permutations. V: A sextuple distribution ⋮ New Eulerian numbers of type \(D\)

Cites Work

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• Permutation statistics of indexed permutations
• Signed permutation statistics
• Signed permutation statistics and cycle type
• Eulerian calculus. I: Univariable statistics
• \(q\)-Eulerian polynomials arising from Coxeter groups
• Major and descent statistics for the even-signed permutation group
• Eulerian calculus. II: An extension of Han's fundamental transformation
• Eulerian calculus. III: The ubiquitous Cauchy formula
• The distribution of descents and length in a Coxeter group
• Descent numbers and major indices for the hyperoctahedral group

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