Gamma-Positivity for a Refinement of Median Genocchi Numbers

Sen Peng Eu, Tung Shan Fu, Hsin Hao Lai, Yuan Hsun Lo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study the generating function of descent numbers for the permutations with descent pairs of prescribed parities, the distribution of which turns out to be a refinement of median Genocchi numbers. We prove the γ-positivity for the polynomial and derive the generating function for the γ-vectors, expressed in the form of continued fraction. We also come up with an artificial statistic that gives a q-analogue of the γ-positivity for the permutations with descents only allowed from an odd value to an odd value.

Original languageEnglish
Article numberP2.15
JournalElectronic Journal of Combinatorics
Volume29
Issue number2
DOIs
Publication statusPublished - 2022

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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