DMTCS Proceedings, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)

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Multi-cluster complexes

Cesar Ceballos, Jean-Philippe Labbé, Christian Stump


We present a family of simplicial complexes called multi-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.

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