Subword complexes, cluster complexes, and generalized multi-associahedra

Journal of Algebraic Combinatorics: An International Journal, no. 1 (2014): 17-51

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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聽k, a聽spherical subword complex called multi-cluster complex. For聽k=1, we show that this subword complex is isomorphic to the cluster complex o...More

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