The combinatorics of twisted involutions in Coxeter groups

Details The combinatorics of twisted involutions in Coxeter groups The combinatorics of twisted involutions in Coxeter groups

2004-11-19

arxiv.org/abs/math/0411429v2

Mathematics

Combinatorics

12 pages; minor revisions, to appear in TAMS

Scientific paper

The open intervals in the Bruhat order on twisted involutions in a Coxeter group are shown to be PL spheres. This implies results conjectured by F. Incitti and sharpens the known fact that these posets are Gorenstein* over Z_2. We also introduce a Boolean cell complex which is an analogue for twisted involutions of the Coxeter complex. Several classical Coxeter complex properties are shared by our complex. When the group is finite, it is a shellable sphere, shelling orders being given by the linear extensions of the weak order on twisted involutions. Furthermore, the h-polynomial of the complex coincides with the polynomial counting twisted involutions by descents. In particular, this gives a type independent proof that the latter is symmetric.

Affiliated with

Also associated with

No associations

Rating

The combinatorics of twisted involutions in Coxeter groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The combinatorics of twisted involutions in Coxeter groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The combinatorics of twisted involutions in Coxeter groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-85453