Bruhat-Chevalley order on the rook monoid

Details Bruhat-Chevalley order on the rook monoid Bruhat-Chevalley order on the rook monoid

2008-03-04

arxiv.org/abs/0803.0491v2

Mathematics

Combinatorics

21 pages. New references are added

Scientific paper

The 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 $R_n$.

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