Wilf's Conjecture

Abstract

In a Note in this Monthly, Klazar raised the question of whether the alternating sum of the Stirling numbers of the second kind $B^{\pm }(n)={\sum }_{k=0}^n(-1{)}^{k}S(n,k)$ is ever zero for $n\ne 2$. In this article, we present an exposition of the history of this problem, and an economical account of a recent proof that there is at most one $n\ne 2$ for which $B^{\pm }(n)=0$.

19 page, 1 figure

Cited by in corpus (2)

• Refinements of the Bell and Stirling numbers
• Quadratic fields, Artin-Schreier extensions, and Bell numbers