Total positivity for cominuscule Grassmannians
| dc.creator | Lam, Thomas | |
| dc.creator | Williams, Lauren | |
| dc.date | 2007-10-16 | |
| dc.date.accessioned | 2026-07-07T08:36:33Z | |
| dc.date.available | 2026-07-07T08:36:33Z | |
| dc.description | In this paper we explore the combinatorics of the non-negative part (G/P)+ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams -- certain fillings of generalized Young diagrams which are in bijection with the cells of (G/P)+. In the classical cases, we describe Le-diagrams explicitly in terms of pattern avoidance. We also define a game on diagrams, by which one can reduce an arbitrary diagram to a Le-diagram. We give enumerative results and relate our Le-diagrams to other combinatorial objects. Surprisingly, the totally non-negative cells in the open Schubert cell of the odd and even orthogonal Grassmannians are (essentially) in bijection with preference functions and atomic preference functions respectively. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/0710.2932 | |
| dc.identifier | http://arxiv.org/abs/0710.2932 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140103 | |
| dc.subject | Combinatorics | |
| dc.title | Total positivity for cominuscule Grassmannians | |
| dc.type | text |