On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5
| dc.creator | Berkovich, Alexander | |
| dc.creator | Garvan, Frank G. | |
| dc.date | 2004-01-03 | |
| dc.date.accessioned | 2026-07-07T05:04:20Z | |
| dc.date.available | 2026-07-07T05:04:20Z | |
| dc.description | In a recent study of sign-balanced, labelled posets Stanley [13], introduced a new integral partition statistic srank(pi) = O(pi) - O(pi'), where O(pi) denotes the number of odd parts of the partition pi and pi' the conjugate of pi. In [1] Andrews proved the following refinement of Ramanujan's partition congruence mod 5: p[0](5n +4) = p[2](5n + 4) = 0 (mod 5), p(n) = p[0](n) + p[2](n), where p[i](n) (i = 0, 2) denotes the number of partitions of n with srank = i (mod 4) and p(n) is the number of unrestricted partitions of n. Andrews asked for a partition statistic that would divide the partitions enumerated by p[i](5n + 4) (i = 0, 2) into five equinumerous classes. In this paper we discuss two such statistics. The first one, while new, is intimately related to the Andrews-Garvan [2] crank. The second one is in terms of the 5-core crank, introduced by Garvan, Kim and Stanton [9]. Finally, we discuss some new formulas for partitions that are 5-cores. | |
| dc.description | 14 pages, 1 figure, 2 tables | |
| dc.identifier | https://arxiv.org/abs/math/0401012 | |
| dc.identifier | http://arxiv.org/abs/math/0401012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69766 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11P81, 11P83, 05A17, 05A19 | |
| dc.title | On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5 | |
| dc.type | text |