Authors: MAHİR BİLEN CAN, LEX E. RENNER
Abstract: 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 . 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.
Keywords: Rook monoid, Deodhar ordering, Bruhat-Chevalley ordering, Borel orbits
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