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Bruhat-Chevalley order on the rook monoid by Can, Mahir Bilen; Renner, Lex E. is a scholarly article available to read on EtoBox.

What is Bruhat-Chevalley order on the rook monoid about?

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 $R_n$.

Author

Can, Mahir Bilen; Renner, Lex E.

Published

2008

Language

EN