English

Counting symmetric and non-symmetric peaks in a set partition

Combinatorics 2024-08-21 v3

Abstract

The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of [n][n] with exactly kk blocks, and the second one is the total number of non-symmetric peaks in a set partition of [n][n] with exactly kk blocks. We represent these results in two ways. First by using the theory of generating functions, and the second by using combinatorial tools.

Keywords

Cite

@article{arxiv.2401.01687,
  title  = {Counting symmetric and non-symmetric peaks in a set partition},
  author = {Walaa Asakly and Noor Kezil},
  journal= {arXiv preprint arXiv:2401.01687},
  year   = {2024}
}