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Turkish Journal of Mathematics

DOI

10.3906/mat-1009-54

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 [1]. 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.

First Page

499

Last Page

519

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