@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 = "Funding Information: The authors thank the referees for reading the manuscript carefully and providing helpful suggestions. The authors were supported in part by Ministry of Science and Technology (MOST), Taiwan under grants 110-2115-M-003-011-MY3 (S.-P. Eu), 109-2115-M-153-004-MY2 (T.-S. Fu), 108-2115-M-017-004 (H.-H. Lai), and 110-2115-M-153-004-MY2 (Y.-H. Lo). 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",
}