TY - JOUR
T1 - Elementary proofs of various facts about 3-cores
AU - Hirschhorn, Michael D.
AU - Sellers, James A.
PY - 2009/6
Y1 - 2009/6
N2 - 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).
AB - 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).
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U2 - 10.1017/S0004972709000136
DO - 10.1017/S0004972709000136
M3 - Article
AN - SCOPUS:77957235012
SN - 0004-9727
VL - 79
SP - 507
EP - 512
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -