2021/02/17 by Zhao, Tongyuan, Sun, Yue, Zhao, Feng
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.08508
A ballot permutation is a permutation π such that in any prefix of π 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.