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 O k,i (n) be the number of overpartitions of n whose parts satisfy certain difference condition and P k,i (n) be the number of overpartitions of n whose non-overlined parts satisfy certain congruence condition. We show that O k,i (n) = P k,i (n) for 1 ≤ i < k.