Posets related to the connectivity set of Coxeter groups
Combinatorics
2010-03-31 v3
Abstract
We define the notion of connectivity set for elements of any finitely generated Coxeter group. Then we define an order related to this new statistic and show that the poset is graded and each interval is a shellable lattice. This implies that any interval is Cohen-Macauley. We also give a Galois connection between intervals in this poset and a boolean poset. This allows us to compute the Mobius function for any interval.
Keywords
Cite
@article{arxiv.math/0509271,
title = {Posets related to the connectivity set of Coxeter groups},
author = {Nantel Bergeron and Christophe Hohlweg and Mike Zabrocki},
journal= {arXiv preprint arXiv:math/0509271},
year = {2010}
}
Comments
13 pages; 4 figures; final version; accepted in Journal of Algebra