The Eulerian distribution on involutions is indeed \(\gamma\)-positive

DOI10.1016/j.jcta.2019.02.004zbMath1414.05020arXiv1808.08481OpenAlexW2963181386MaRDI QIDQ2424907

Danielle Wang

Publication date: 25 June 2019

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

Full work available at URL: https://arxiv.org/abs/1808.08481

zbMATH Keywords

involutionsdescent number\(\gamma\)-positivityseparable permutationsEulerian polynomial

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Permutations, words, matrices (05A05) Special sequences and polynomials (11B83)

Related Items

The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group ⋮ The Eulerian distribution on \(k\)-colored involutions ⋮ David-Barton type identities and alternating run polynomials ⋮ The Eulerian distribution on the involutions of the hyperoctahedral group is indeed \(\gamma \)-positive ⋮ Refined Wilf-equivalences by Comtet statistics ⋮ \(\gamma\)-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

Cites Work

• Proof of Gessel's \(\gamma\)-positivity conjecture
• On \(\gamma\)-positive polynomials arising in pattern avoidance
• The \(\gamma\)-positivity of basic Eulerian polynomials via group actions
• Patterns in permutations and words.
• The symmetric and unimodal expansion of Eulerian polynomials via continued fractions
• On two unimodal descent polynomials
• Faces of generalized permutohedra
• Forbidden subsequences
• A sextuple equidistribution arising in pattern avoidance
• Actions on permutations and unimodality of descent polynomials
• The Eulerian distribution on involutions is indeed unimodal
• Théorie géométrique des polynômes eulériens
• Unimodality, log-concavity, real-rootedness and beyond