The Rogers–Ramanujan–Gordon identities, the generalized Göllnitz–Gordon identities, and parity questions

Abstract

Recently, George Andrews investigated a variety of parity questions in classical partition identities. In particular, he involved parity restrictions in the Rogers–Ramanujan–Gordon identities. In this paper, we reveal the relationship of his results with Bressoudʼs generalization of the Rogers–Ramanujan–Gordon identities. In addition, Andrews observed that one case of his identities is related to the Göllnitz–Gordon identities. In the light of the fact that the Göllnitz–Gordon identities are special cases of a general partition theorem of Andrews, we extend Andrewsʼ identities by generalizing his observation. We also provide a generating function of the missing case of his identities.