2022/06/21 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1
Mathematics · #11B73 #11B83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2206.10194
openalex publication_date 2022/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any positive integer r, the r-associated Stirling number of the second kind enumerates the number of partitions of the set1,2,3,...,n into k non-empty disjoint subsets such that each subset contains at least r elements. We introduce the degenerate r-associated Stirling numbers of the second kind and of the first kind. They are degenerate versions of the r-associated Stirling numbers of the second kind and of the first kind, and reduce to the degenerate Stirling numbers of the second kind and of the first kind for r=1. The aim of this paper is to derive recurrence relations for both of those numbers.