Faces of generalized cluster complexes and noncrossing partitions
| dc.creator | Tzanaki, E. | |
| dc.date | 2006-05-31 | |
| dc.date | 2006-07-10 | |
| dc.date.accessioned | 2026-07-07T07:14:40Z | |
| dc.date.available | 2026-07-07T07:14:40Z | |
| dc.description | Let $Φ$ be an finite root system with corresponding reflection group $W$ and let $m$ be a nonnegative integer. We consider the generalized cluster complex $Δ^m(Φ)$ defined by S. Fomin and N. Reading and the poset $NC_{(m)}(W)$ of $m$-divisible noncrossing partitions defined by D. Armstrong. We give a characterization of the faces of $Δ^m(Φ)$ in terms of $NC_{(m)}(W)$, generalizing that of T. Brady and C. Watt given in the case $m=1$. Making use of this, we give a case free proof of a conjecture of F. Chapoton and D. Armstrong, which relates a certain refined face count of $Δ^m(Φ)$ with the Möbius function of $NC_{(m)}(W)$. | |
| dc.description | second version | |
| dc.identifier | https://arxiv.org/abs/math/0605785 | |
| dc.identifier | http://arxiv.org/abs/math/0605785 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112974 | |
| dc.subject | Combinatorics | |
| dc.title | Faces of generalized cluster complexes and noncrossing partitions | |
| dc.type | text |