The Rook Monoid is Lexicographically Shellable
Mahir Bilen Can
TL;DR
This paper proves that the rook monoid's Bruhat-Chevalley-Renner order is EL-shellable and characterizes the topological structure of its order complex.
Contribution
It establishes the EL-shellability of the rook monoid's order and determines the order complex's homeomorphism type, advancing combinatorial and topological understanding.
Findings
Proved the rook monoid's order is EL-shellable
Determined the order complex's homeomorphism type
Enhanced understanding of rook monoid's combinatorial structure
Abstract
We prove that the Bruhat-Chevalley-Renner order on the rook monoid is EL-shellable. We determine the homeomorphism type of the associated order complex.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.