ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES

By Michael D. Hirschhorn, James A. Sellers. 2009

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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 3nC 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, a3.4nC 1/D a3.n/. 2000 Mathematics subject classification: primary 05A17, 11P81, 11P83.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

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