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 Bressoud's 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 Andrews' identities by generalizing his observation. We also provide a generating function of the missing case of his identities.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics