Elementary proofs of various facts about 3-cores

Michael D. Hirschhorn; James A. Sellers

doi:10.1017/S0004972709000136

Elementary proofs of various facts about 3-cores

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

Using elementary means, we derive an explicit formula for a₃(n), the number of 3-core partitions of n, in terms of the prime factorization of 3n+1. Based on this result, we are able to prove several infinite families of arithmetic results involving a₃(n), one of which specializes to the recent result of Baruah and Berndt which states that, for all n ≥ 0, a ₃(4n+1)=a₃(n).

Original language	English (US)
Pages (from-to)	507-512
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	79
Issue number	3
DOIs	https://doi.org/10.1017/S0004972709000136
State	Published - Jun 2009
Externally published	Yes

Keywords

3-cores
Jacobis Triple Product Identity
Lambert series
congruences
generating function
partition

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Elementary proofs of various facts about 3-cores

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Keywords

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