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- Title
ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES.
- Authors
Hirschhorn, Michael D.; Sellers, James A.
- 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, a3(4n + 1) = a3(n).
- Subjects
FACTORIZATION of operators; FACTORIZATION; FACTOR tables; MATHEMATICAL proofs; JACOBI identity; TOPOLOGICAL algebras; SET theory; PROOF theory; NUMERICAL solutions to equations
- Publication
Bulletin of the Australian Mathematical Society, 2009, Vol 79, Issue 3, p507
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972709000136