English

Counting with Borel's Triangle

Combinatorics 2018-04-06 v1

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.

Keywords

Cite

@article{arxiv.1804.01597,
  title  = {Counting with Borel's Triangle},
  author = {Yue Cai and Catherine Yan},
  journal= {arXiv preprint arXiv:1804.01597},
  year   = {2018}
}
R2 v1 2026-06-23T01:14:13.115Z