On a conjecture of Wilf
Number Theory
2021-02-03 v2 Combinatorics
Abstract
Let n and k be natural numbers and let S(n,k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum \sum_{j=0}^{n} (-1)^{j} S(n,j) is nonzero for all n>2. We prove this conjecture for all n not congruent to 2 and not congruent to 2944838 modulo 3145728 and discuss applications of this result to graph theory, multiplicative partition functions, and the irrationality of p-adic series.
Keywords
Cite
@article{arxiv.math/0608085,
title = {On a conjecture of Wilf},
author = {Stefan de Wannemacker and Thomas Laffey and Robert Osburn},
journal= {arXiv preprint arXiv:math/0608085},
year = {2021}
}
Comments
18 pages, final version, accepted for publication in the Journal of Combinatorial Theory, Series A