Hook lengths and 3-cores

2008/05/16 by Guo-Niu Han, Ken Ono, Han, Guo-Niu +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0805.2461

openalex publication_date 2008/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• On simultaneous (s, s+t, s+2t, …)-core partitions

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