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 $\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain difference condition and $\widetilde{P}_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruence condition. We show that $\widetilde{O}_{k,i}(n) = \widetilde{P}_{k,i}(n)$ for $1 \leq i \lt k$.