p-adic Stirling numbers of the second kind
Number Theory
2013-07-30 v1 Combinatorics
Abstract
Let S(n,k) denote the Stirling numbers of the second kind. We prove that the p-adic limit of S(p^e a + c, p^e b + d) as e goes to infinity exists for all integers a, b, c, and d. We call the limiting p-adic integer S(p^\infty a + c, p^\infty b + d). When a equiv b mod (p-1) or d \le 0, we express them in terms of p-adic binomial coefficients introduced in a recent paper.
Keywords
Cite
@article{arxiv.1307.7687,
title = {p-adic Stirling numbers of the second kind},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:1307.7687},
year = {2013}
}
Comments
13 pages