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 $B^\pm(n)=\sum_{k=0}^n(-1)^kS(n,k)$ is ever zero for $n\neq 2$. 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 $n\neq 2$ for which $B^\pm(n)=0$.