The Bressoud-Göllnitz-Gordon Theorem for Overpartitions of even moduli

2017/02/28 by He, Thomas Y., Wang, Allison Y. F., Zhao, Alice X. H.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.08621

Abstract

We give an overpartition analogue of Bressoud's combinatorial generalization of the Göllnitz-Gordon theorem for even moduli in general case. Let \widetildeO_k,i(n) be the number of overpartitions of n whose parts satisfy certain difference condition and \widetildeP_k,i(n) be the number of overpartitions of n whose non-overlined parts satisfy certain congruence condition. We show that \widetildeO_k,i(n)=\widetildeP_k,i(n) for 1≤ i

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