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

Abstract: We give an overpartition analogue of Bressoud's combinatorial generalization of the G\"ollnitz-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 $1\leq i<k$.