Bruhat-Chevalley order on the rook monoid

Authors

MAHİR BİLEN CAN
LEX E. RENNER

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.

Keywords

Rook monoid, Deodhar ordering, Bruhat-Chevalley ordering, Borel orbits

First Page

499

Last Page

519

Recommended Citation

CAN, MAHİR BİLEN and RENNER, LEX E. (2012) "Bruhat-Chevalley order on the rook monoid," Turkish Journal of Mathematics: Vol. 36: No. 4, Article 1. https://doi.org/10.3906/mat-1009-54
Available at: https://journals.tubitak.gov.tr/math/vol36/iss4/1