Subword complexes, cluster complexes, and generalized multi-associahedra
By Cesar Ceballos, Jean-Philippe Labbé, Christian Stump. 2011
96 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/514c3be43223ba122b2d45d7e1e449b5aae37762
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Algebraic and Geometric Methods in Enumerative Combinatorics (2014, background): “n, which is topologically a sphere [Jon03]; it is not currently known whether it is polytopal. There is a further generalization in the context of Coxeter groups, with connections to cluster algebras [CLS14]. (c) These determinants also arise naturally in the commutative algebraic properties of Pfaf”