A two-sided analogue of the Coxeter complex
For any Coxeter system (W, S) of rank n, we introduce an abstract boolean complex (simplicial poset) of dimension 2n − 1 which contains the Coxeter complex as a relative subcomplex. Faces are indexed by triples (J,w,K), where J and K are subsets of the set S of simple generators, and w is a minimal...
Uložené v:
| Vydané v: | Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th... |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Predmet: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | For any Coxeter system (W, S) of rank n, we introduce an abstract boolean complex (simplicial poset) of dimension 2n − 1 which contains the Coxeter complex as a relative subcomplex. Faces are indexed by triples (J,w,K), where J and K are subsets of the set S of simple generators, and w is a minimal length representative for the double parabolic coset WJ wWK . There is exactly one maximal face for each element of the group W . The complex is shellable and thin, which implies the complex is a sphere for the finite Coxeter groups. In this case, a natural refinement of the h-polynomial is given by the “two-sided” W -Eulerian polynomial, i.e., the generating function for the joint distribution of left and right descents in W . |
|---|---|
| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6353 |