Degenerate r-associated Stirling numbers

Abstract

For any positive integer r, the r-associated Stirling number of the second kind S (r) 2 (n, k) enumerates the number of partitions of the set {1, 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. 2010 Mathematics Subject Classification. 11B73; 11B83. Key words and phrases. degenerate r-associated Stirling numbers of the second kind; degenerate r-associated Stirling numbers of the first kind; degenerate r-associated Bell polynomials.