On the sign-imbalance of partition shapes
| dc.creator | Sjöstrand, Jonas | |
| dc.date | 2003-09-15 | |
| dc.date | 2005-09-30 | |
| dc.date.accessioned | 2026-07-07T06:19:52Z | |
| dc.date.available | 2026-07-07T06:19:52Z | |
| dc.description | Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2^[n/2]. We present a stronger theorem with a purely combinatorial proof using the Robinson-Schensted correspondence and a new concept called chess tableaux. We also prove a sharpening of another conjecture by Stanley concerning weighted sums of squares of sign-imbalances. The proof is built on a remarkably simple relation between the sign of a permutation and the signs of its RS-corresponding tableaux. | |
| dc.description | 12 pages. Better presentation | |
| dc.identifier | https://arxiv.org/abs/math/0309231 | |
| dc.identifier | http://arxiv.org/abs/math/0309231 | |
| dc.identifier | Journal of Combinatorial Theory, Series A 111 (2005) 190-203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95175 | |
| dc.subject | Combinatorics | |
| dc.subject | 06A07; 05E10 | |
| dc.title | On the sign-imbalance of partition shapes | |
| dc.type | text |