Counting with Borel's Triangle

2018/04/04 by Cai, Yue, Yan, Catherine
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.01597

Abstract

Borel's triangle is an array of integers closely related to the classical Catalan numbers. In this paper we study combinatorial statistics counted by Borel's triangle. We present various combinatorial interpretations of Borel's triangle in terms of lattice paths, binary trees, and pattern avoiding permutations and matchings, and derive a functional equation that is useful in analyzing the involved structures.

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