## Ceballos, Cesar and Labbé, Jean-Philippe and Stump, Christian - Multi-cluster complexes

dmtcs:3014 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Multi-cluster complexes

Authors: Ceballos, Cesar and Labbé, Jean-Philippe and Stump, Christian

We present a family of simplicial complexes called \emphmulti-cluster complexes. These complexes generalize the concept of cluster complexes, and extend the notion of multi-associahedra of types ${A}$ and ${B}$ to general finite Coxeter groups. We study combinatorial and geometric properties of these objects and, in particular, provide a simple combinatorial description of the compatibility relation among the set of almost positive roots in the cluster complex.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: multi-triangulations, Coxeter―Catalan combinatorics, sorting words,Subword complexes, cluster complexes, generalized associahedra,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]