Refined Eulerian numbers and ballot permutations
Combinatorics
2021-02-18 v1
Abstract
A ballot permutation is a permutation {\pi} such that in any prefix of {\pi} the descent number is not more than the ascent number. In this article, we obtained a formula in close form for the multivariate generating function of {A(n,d,j)}, which denote the number of permutations of length n with d descents and j as the first letter. Besides, by a series of calculations with generatingfunctionology, we confirm a recent conjecture of Wang and Zhang for ballot permutations.
Cite
@article{arxiv.2102.08508,
title = {Refined Eulerian numbers and ballot permutations},
author = {Tongyuan Zhao and Yue Sun and Feng Zhao},
journal= {arXiv preprint arXiv:2102.08508},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:2009.05973