A bijection between dominant Shi regions and core partitions
| dc.creator | Fishel, Susanna | |
| dc.creator | Vazirani, Monica | |
| dc.date | 2009-04-20 | |
| dc.date.accessioned | 2026-07-07T13:06:45Z | |
| dc.date.available | 2026-07-07T13:06:45Z | |
| dc.description | It is well-known that Catalan numbers $C_n = \frac{1}{n+1} \binom{2n}{n}$ count the number of dominant regions in the Shi arrangement of type $A$, and that they also count partitions which are both $n$-cores as well as $(n+1)$-cores. These concepts have natural extensions, which we call here the $m$-Catalan numbers and $m$-Shi arrangement. In this paper, we construct a bijection between dominant regions of the $m$-Shi arrangement and partitions which are both $n$-cores as well as $(mn+1)$-cores. The bijection is natural in the sense that it commutes with the action of the affine symmetric group. | |
| dc.identifier | https://arxiv.org/abs/0904.3118 | |
| dc.identifier | http://arxiv.org/abs/0904.3118 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227880 | |
| dc.subject | Combinatorics | |
| dc.title | A bijection between dominant Shi regions and core partitions | |
| dc.type | text |