Gamma-Positivity for a Refinement of Median Genocchi Numbers

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

doi:10.37236/10312

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (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 language	English
Article number	P2.15
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	2
DOIs	https://doi.org/10.37236/10312
Publication status	Published - 2022

ASJC Scopus subject areas

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

Access to Document

10.37236/10312

Cite this

@article{d350bc69216a4fa4bbebe41036c0b3cd,

title = "Gamma-Positivity for a Refinement of Median Genocchi Numbers",

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.",

author = "Eu, {Sen Peng} and Fu, {Tung Shan} and Lai, {Hsin Hao} and Lo, {Yuan Hsun}",

note = "Publisher Copyright: {\textcopyright} The authors.",

year = "2022",

doi = "10.37236/10312",

language = "English",

volume = "29",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "2",

}

TY - JOUR

T1 - Gamma-Positivity for a Refinement of Median Genocchi Numbers

AU - Eu, Sen Peng

AU - Fu, Tung Shan

AU - Lai, Hsin Hao

AU - Lo, Yuan Hsun

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85128770210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85128770210&partnerID=8YFLogxK

U2 - 10.37236/10312

DO - 10.37236/10312

M3 - Article

AN - SCOPUS:85128770210

SN - 1077-8926

VL - 29

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 2

M1 - P2.15

ER -

Gamma-Positivity for a Refinement of Median Genocchi Numbers

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this