2016/12/15 by He, Thomas Y., Ji, Kathy Q., Wang, Allison Y. F. +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1612.04960
In 1967, Andrews found a combinatorial generalization of the Göllnitz-Gordon theorem, which can be called the Andrews-Göllnitz-Gordon theorem. In 1980, Bressoud derived a multisum Rogers-Ramanujan-type identity, which can be considered as the generating function counterpart of the Andrews-Göllnitz-Gordon theorem. Lovejoy gave an overpartition analogue of the Andrews-Göllnitz-Gordon theorem for i=k. In this paper, we give an overpartition analogue of this theorem in the general case. By using Bailey's lemma and a change of base formula due to Bressoud, Ismail and Stanton, we obtain an overpartition analogue of Bressoud's identity. We then give a combinatorial interpretation of this identity by introducing the Göllnitz-Gordon marking of an overpartition, which yields an overpartition analogue of the Andrews-Göllnitz-Gordon theorem.