A bijection on core partitions and a parabolic quotient of the affine symmetric group
| dc.creator | Berg, Chris | |
| dc.creator | Jones, Brant | |
| dc.creator | Vazirani, Monica | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T09:31:16Z | |
| dc.date.available | 2026-07-07T09:31:16Z | |
| dc.description | Let $\ell,k$ be fixed positive integers. In an earlier work, the first and third authors established a bijection between $\ell$-cores with first part equal to $k$ and $(\ell-1)$-cores with first part less than or equal to $k$. This paper gives several new interpretations of that bijection. The $\ell$-cores index minimal length coset representatives for $\widetilde{S_{\ell}} / S_{\ell}$ where $\widetilde{S_{\ell}}$ denotes the affine symmetric group and $S_{\ell}$ denotes the finite symmetric group. In this setting, the bijection has a beautiful geometric interpretation in terms of the root lattice of type $A_{\ell-1}$. We also show that the bijection has a natural description in terms of another correspondence due to Lapointe and Morse. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0804.1380 | |
| dc.identifier | http://arxiv.org/abs/0804.1380 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158398 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E10 | |
| dc.title | A bijection on core partitions and a parabolic quotient of the affine symmetric group | |
| dc.type | text |