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 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1038-1056 |
| Number of pages | 19 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 120 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2013.07 |
Keywords
- Integer partitions
- Parity in partitions
- The Göllnitz-Gordon identities
- The Rogers-Ramanujan identities
- The Rogers-Ramanujan-Gordon identities
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