A note on the subword complexes in Coxeter groups

Details A note on the subword complexes in Coxeter groups A note on the subword complexes in Coxeter groups

2008-11-28

arxiv.org/abs/0811.4552v1

Mathematics

Commutative Algebra

Scientific paper

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.

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