A note on the subword complexes in Coxeter groups
Commutative Algebra
2008-12-01 v1 Combinatorics
Abstract
We prove that the Stanley--Reisner ideal of the Alexander dual of the subword complexes in Coxeter groups has linear quotients with respect to the lexicographical order of the minimal monomial generators. As a consequence, we obtain a shelling order on the facets of the subword complex. We relate some invariants of the subword complexes or of their dual with invariants of the word. For a particular class of subword complexes, we prove that the Stanley--Reisner ring is a complete intersection ring.
Cite
@article{arxiv.0811.4552,
title = {A note on the subword complexes in Coxeter groups},
author = {Anda Olteanu},
journal= {arXiv preprint arXiv:0811.4552},
year = {2008}
}