dc.contributor.author | Lam, Thomas | |
dc.contributor.author | Williams, Lauren | |
dc.date.accessioned | 2009-04-18T02:38:01Z | |
dc.date.issued | 2008 | |
dc.identifier.citation | Lam, Thomas, and Lauren Williams. 2008. Total positivity for cominuscule Grassmannians. New York Journal of Mathematics 14. | en |
dc.identifier.issn | 1076-9803 | en |
dc.identifier.uri | http://nrs.harvard.edu/urn-3:HUL.InstRepos:2796935 | |
dc.description.abstract | 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. | en |
dc.description.sponsorship | Mathematics | en |
dc.language.iso | en_US | en |
dc.publisher | SUNY Albany | en |
dc.relation.hasversion | http://arxiv.org/abs/0710.2932 | en |
dash.license | LAA | |
dc.title | Total positivity for cominuscule Grassmannians | en |
dc.relation.journal | New York Journal of Mathematics | en |
dash.depositing.author | Lam, Thomas | |
dash.contributor.affiliated | Williams, Lauren | |
dash.contributor.affiliated | Lam, Thomas | |