2025/10/07 by Asakly, Walaa, Kezil, Noor
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.06521
In this paper, we aim to derive an explicit formula for the total number of elements preceding records over all set partitions of [n] with exactly k blocks, as well as an asymptotic estimate for the total sum of elements preceding records in all set partitions of [n], expressed in terms of Bell numbers. To achieve this, we analyze the generating function that enumerates set partitions of [n] according to this statistic, which we denote by \sumelements.