%0 Journal Article
%T The rook monoid is lexicographically shellable
%A Mahir Bilen Can
%J Mathematics
%D 2010
%I arXiv
%X The main result of this paper is that the rook monoid $R_n$ with respect to Bruhat-Chevalley-Renner ordering is a lexicographically shellable poset. Consequently, we know that for any interval $I$ in $R_n$, the order complex $\Delta(I)$ has the homotopy type of a wedge of spheres or balls.
%U http://arxiv.org/abs/1001.5104v1