Partitions weighted by the parity of the crank
| dc.creator | Choi, Dohoon | |
| dc.creator | Kang, Soon-Yi | |
| dc.creator | Lovejoy, Jeremy | |
| dc.date | 2007-03-09 | |
| dc.date.accessioned | 2026-07-07T07:51:11Z | |
| dc.date.available | 2026-07-07T07:51:11Z | |
| dc.description | A partition statistic ` crank' gives combinatorial interpretations for Ramanujan's famous partition congruences. In this paper, we establish an asymptotic formula, Ramanujan type congruences, and q-series identities that the number of partitions with even crank $M_e(n)$ minus the number of partitions with odd crank $M_o(n)$ satisfies. For example, we show that $M_e(5n+4)-M_o(5n+4)\equiv 0 \pmod 5.$ We also determine the exact values of $M_e(n)-M_o(n)$ in case of partitions into distinct parts, which are at most two and zero for infinitely many $n$. | |
| dc.identifier | https://arxiv.org/abs/math/0703266 | |
| dc.identifier | http://arxiv.org/abs/math/0703266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125422 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11P81, 11P82, 11P83, 05A17, 33D15, 11F11 | |
| dc.title | Partitions weighted by the parity of the crank | |
| dc.type | text |