Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1009-54
Keywords
Rook monoid, Deodhar ordering, Bruhat-Chevalley ordering, Borel orbits
First Page
499
Last Page
519
Recommended Citation
CAN, M. B, & RENNER, L. E (2012). Bruhat-Chevalley order on the rook monoid. Turkish Journal of Mathematics 36 (4): 499-519. https://doi.org/10.3906/mat-1009-54
