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Abstract: Recently, the first author generalized a formula of Nekrasov and Okounkovwhich gives a combinatorial formula, in terms of hook lengths of partitions,for the coefficients of certain power series. In the course of thisinvestigation, he conjectured that $A000731n=0$ if and only if$A033687n=0$. The numbers $A000731n$ are given in terms of hook lengths ofpartitions, while $A033687n$ equals the number of 3-core partitions of $n$.Here we prove this conjecture.



Author: Guo-Niu Han, Ken Ono

Source: https://arxiv.org/







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