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arXiv · 0805.2461

Hook lengths and 3-cores

Guo-Niu Han·Ken Ono
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Abstract

Recently, the first author generalized a formula of Nekrasov and Okounkov which gives a combinatorial formula, in terms of hook lengths of partitions, for the coefficients of certain power series. In the course of this investigation, he conjectured that $A000731(n)=0$ if and only if $A033687(n)=0$. The numbers $A000731(n)$ are given in terms of hook lengths of partitions, while $A033687(n)$ equals the number of 3-core partitions of $n$. Here we prove this conjecture.

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Guo-Niu Han, Ken Ono. 2008-05-16. Hook lengths and 3-cores. https://arxiv.org/abs/0805.2461

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