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arXiv · 2305.08046

Wilf's Conjecture

Valerio De Angelis·Dominic Marcello
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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 $B^\pm(n)=0$.

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Valerio De Angelis, Dominic Marcello. 2023-05-14. Wilf's Conjecture. https://doi.org/10.4169/amer.math.monthly.123.6.557

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