The combinatorics of twisted involutions in Coxeter groups
2005 (English)In: FPSAC Proceedings 2005: 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics, 2005, 195-206 p.Conference paper (Refereed)
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.
Place, publisher, year, edition, pages
2005. 195-206 p.
IdentifiersURN: urn:nbn:se:kth:diva-148560ScopusID: 2-s2.0-84861169870OAI: oai:DiVA.org:kth-148560DiVA: diva2:737032
17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05; Taormina, Italy, 20-25 June, 2005
QC 201408112014-08-112014-08-082014-08-11Bibliographically approved