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math.CO2021★ 2 cited
A decomposition of ballot permutations, pattern avoidance and Gessel walks
Zhicong Lin, David G. L. Wang, Tongyuan Zhao
A permutation whose any prefix has no more descents than ascents is called a ballot permutation. In this paper, we present a decomposition of ballot permutations that enables us to…
math.CO2021
Refined Eulerian numbers and ballot permutations
Tongyuan Zhao, Yue Sun, Feng Zhao
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…