Goellnitz-Gordon partitions with weights and parity conditions
| dc.creator | Alladi, Krishnaswami | |
| dc.creator | Berkovich, Alexander | |
| dc.date | 2004-03-10 | |
| dc.date.accessioned | 2026-07-07T05:06:16Z | |
| dc.date.available | 2026-07-07T05:06:16Z | |
| dc.description | A Goellnitz-Gordon partition is one in which the parts differ by at least 2, and where the inequality is strict if a part is even. Let Q_i(n) denote the number of partitions of n into distinct parts not congruent to i mod 4. By attaching weights which are powers of 2 and imposing certain parity conditions on Goellnitz-Gordon partitions, we show that these are equinumerous with Q_i(n) for i=0,2. These complement results of Goellnitz on Q_i(n) for i=1,3, and of Alladi who provided a uniform treatment of all four Q_i(n), i=0,1,2,3, in terms of weighted partitions into parts differing by >= 4. Our approach here provides a uniform treatment of all four Q_i(n) in terms of certain double series representations. These double series identities are part of a new infinite hierarchy of multiple series identities. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403167 | |
| dc.identifier | http://arxiv.org/abs/math/0403167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70410 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11P83, 11P81; 05A19 | |
| dc.title | Goellnitz-Gordon partitions with weights and parity conditions | |
| dc.type | text |