2011/08/31 by Cesar Ceballos, Jean-Philippe Labbé, Christian Stump
Mathematics · #Abstract simplicial complex #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Cluster (spacecraft) #Coxeter element #Coxeter group #Face (sociological concept) #Homotopy and Cohomology in Algebraic Topology #Integer (computer science) #Longest element of a Coxeter group #Simplicial complex #math.CO #msc:05E45 #msc:13F60 #msc:20F55
paper · pdf · doi:10.1007/s10801-013-0437-x
26 pages, 3 Tables, 2 Figures; final version
arxiv created 2013/02/27 · openalex publication_date 2013/03/12 · arxiv updated 2013/07/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called multi-cluster complex. For k=1, we show that this subword complex is isomorphic to the cluster complex of the given type. We show that multi-cluster complexes of types A and B coincide with known simplicial complexes, namely with the simplicial complexes of multi-triangulations and centrally symmetric multi-triangulations respectively. Furthermore, we show that the multi-cluster complex is universal in the sense that every spherical subword complex can be realized as a link of a face of the multi-cluster complex.