New Identities for 7-cores with prescribed BG-rank
| dc.creator | Berkovich, Alexander | |
| dc.creator | Yesilyurt, Hamza | |
| dc.date | 2006-03-06 | |
| dc.date | 2007-09-15 | |
| dc.date.accessioned | 2026-07-07T08:29:24Z | |
| dc.date.available | 2026-07-07T08:29:24Z | |
| dc.description | A q-series with nonnegative power series coefficients is called positive. The partition statistics BG-rank is defined as an alternating sum of parities of parts of a partition. It is known that the generating function for the number of partitions of n that are 7-cores with given BG-rank can be written as certain sum of multi-theta functions. We give explicit representations for these generating functions in terms of sums of positive eta-quotients and derive inequalities for the their coefficients. New identities for the generating function of unrestricted 7-cores and inequalities for their coefficients are also obtained. Our proofs utilize Ramanujan's theory of modular equations. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603150 | |
| dc.identifier | http://arxiv.org/abs/math/0603150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137956 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 05A20, 11F27 | |
| dc.title | New Identities for 7-cores with prescribed BG-rank | |
| dc.type | text |