Sum of elements preceding records in set partitions
Combinatorics
2025-10-09 v1
Abstract
In this paper, we aim to derive an explicit formula for the total number of elements preceding records over all set partitions of with exactly blocks, as well as an asymptotic estimate for the total sum of elements preceding records in all set partitions of , expressed in terms of Bell numbers. To achieve this, we analyze the generating function that enumerates set partitions of according to this statistic, which we denote by .
Keywords
Cite
@article{arxiv.2510.06521,
title = {Sum of elements preceding records in set partitions},
author = {Walaa Asakly and Noor Kezil},
journal= {arXiv preprint arXiv:2510.06521},
year = {2025}
}