The Eulerian distribution on involutions is indeed unimodal

DOI10.1016/j.jcta.2005.10.002zbMath1097.11011arXivmath/0504195OpenAlexW1972070921MaRDI QIDQ2500618

Victor J. W. Guo, Zeng, Jiang

Publication date: 17 August 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504195

zbMATH Keywords

involutionsunimodalityZeilberger's algorithmEulerian polynomialdescent numbers

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Special sequences and polynomials (11B83) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (19)

On \(\gamma\)-positive polynomials arising in pattern avoidance ⋮ Martingales and descent statistics ⋮ The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group ⋮ The Eulerian distribution on involutions is indeed \(\gamma\)-positive ⋮ Positivity of Narayana polynomials and Eulerian polynomials ⋮ The Eulerian distribution on \(k\)-colored involutions ⋮ Plethystic formulas for permutation enumeration ⋮ Descent sets on 321-avoiding involutions and hook decompositions of partitions ⋮ Enumeration of involutions by descents and symmetric matrices ⋮ The symmetric and unimodal expansion of Eulerian polynomials via continued fractions ⋮ Actions on permutations and unimodality of descent polynomials ⋮ Gamma-positivity in combinatorics and geometry ⋮ On two unimodal descent polynomials ⋮ The descent statistic on involutions is not log-concave ⋮ David-Barton type identities and alternating run polynomials ⋮ The Eulerian distribution on the involutions of the hyperoctahedral group is indeed \(\gamma \)-positive ⋮ \(\gamma\)-positivity and partial \(\gamma\)-positivity of descent-type polynomials ⋮ The Eulerian distribution on the involutions of the hyperoctahedral group is unimodal ⋮ Random decompositions of Eulerian statistics

Uses Software

• SARM

Cites Work

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• Permutation statistics on involutions
• Eulerian numbers, tableaux, and the Betti numbers of a toric variety
• On the Neggers-Stanley conjecture and the Eulerian polynomials
• Counting permutations with given cycle structure and descent set
• Sign-graded posets, unimodality of {\(W\)}-polynomials and the {C}harney-{D}avis conjecture
• A note on concavity properties of triangular arrays of numbers
• Fonctions symétriques et séries hypergéométriques basiques multivariées

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