Bruhat-Chevalley order on the rook monoid

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dc.creatorCan, Mahir Bilen
dc.creatorRenner, Lex E.
dc.date2008-03-04
dc.date2008-03-08
dc.date.accessioned2026-07-07T09:25:23Z
dc.date.available2026-07-07T09:25:23Z
dc.descriptionThe rook monoid $R_n$ is the finite monoid whose elements are the 0-1 matrices with at most one nonzero entry in each row and column. The group of invertible elements of $R_n$ is isomorphic to the symmetric group $S_n$. The natural extension to $R_n$ of the Bruhat-Chevalley ordering on the symmetric group is defined in \cite{Renner86}. In this paper, we find an efficient, combinatorial description of the Bruhat-Chevalley ordering on $R_n$. We also give a useful, combinatorial formula for the length function on $R_n$.
dc.description21 pages. New references are added
dc.identifierhttps://arxiv.org/abs/0803.0491
dc.identifierhttp://arxiv.org/abs/0803.0491
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156388
dc.subjectCombinatorics
dc.subjectAlgebraic Geometry
dc.subject20M07; 20H20
dc.titleBruhat-Chevalley order on the rook monoid
dc.typetext

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