Properties of four partial orders on standard Young tableaux
| dc.creator | Taskin, Muge | |
| dc.date | 2005-09-07 | |
| dc.date | 2005-10-03 | |
| dc.date.accessioned | 2026-07-07T06:20:50Z | |
| dc.date.available | 2026-07-07T06:20:50Z | |
| dc.description | Let SYT_n be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYT_n and some of their crucial properties, we prove three main results: (i)Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer. (ii) The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra 2^{[n-1]}. In particular, the Möbius function of these orders on tableaux is (-1)^{n-3}. (iii) For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function. | |
| dc.description | 24 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0509174 | |
| dc.identifier | http://arxiv.org/abs/math/0509174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95425 | |
| dc.subject | Combinatorics | |
| dc.title | Properties of four partial orders on standard Young tableaux | |
| dc.type | text |