Posets related to the connectivity set of Coxeter groups

Details Posets related to the connectivity set of Coxeter groups Posets related to the connectivity set of Coxeter groups

2005-09-13

arxiv.org/abs/math/0509271v3

J. Algebra 303 (2006), no. 2, 831-846

Mathematics

Combinatorics

13 pages; 4 figures; final version; accepted in Journal of Algebra

Scientific paper

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.

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