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

Abstract

We give an overpartition analogue of Bressoud's combinatorial generalization of the Göllnitz-Gordon theorem for even moduli in general case. Let ${\tilde{O}}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain difference condition and ${\tilde{P}}_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruence condition. We show that ${\tilde{O}}_{k,i}(n)={\tilde{P}}_{k,i}(n)$ for $1\le i<k$.

arXiv admin note: text overlap with arXiv:1612.04960