Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes
| dc.creator | Athanasiadis, Christos A. | |
| dc.creator | Tzanaki, Eleni | |
| dc.date | 2006-06-01 | |
| dc.date | 2007-03-15 | |
| dc.date.accessioned | 2026-07-07T07:51:52Z | |
| dc.date.available | 2026-07-07T07:51:52Z | |
| dc.description | Let $Φ$ be a finite root system of rank $n$ and let $m$ be a nonnegative integer. The generalized cluster complex $Δ^m (Φ)$ was introduced by S. Fomin and N. Reading. It was conjectured by these authors that $Δ^m (Φ)$ is shellable and by V. Reiner that it is $(m+1)$-Cohen-Macaulay, in the sense of Baclawski. These statements are proved in this paper. Analogous statements are shown to hold for the positive part $Δ^m_+ (Φ)$ of $Δ^m (Φ)$. An explicit homotopy equivalence is given between $Δ^m_+ (Φ)$ and the poset of generalized noncrossing partitions, associated to the pair $(Φ, m)$ by D. Armstrong. | |
| dc.description | Final version, 10 pages; to appear in Israel Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0606018 | |
| dc.identifier | http://arxiv.org/abs/math/0606018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125671 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 20F55; 05E99 | |
| dc.title | Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes | |
| dc.type | text |