Subword complexes, cluster complexes, and generalized multi-associahedra |
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Authors: | Cesar Ceballos Jean-Philippe Labbé Christian Stump |
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Institution: | 1. Institut für Mathematik, Freie Universit?t Berlin, Arnimallee 2, 14195, Berlin, Germany 2. Institut für Algebra, Zahlentheorie, Diskrete Mathematik, Leibniz Universit?t Hannover, Hannover, Germany
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Abstract: | 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. |
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