NDLI: Subword complexes, cluster complexes, and generalized multi-associahedra

Content Provider	Springer Nature Link
Author	Ceballos, Cesar Labbé, Jean Philippe Stump, Christian
Copyright Year	2013
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.
Starting Page	17
Ending Page	51
Page Count	35
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	39
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2013-03-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Subword complex Cluster complex Generalized associahedron Multi-triangulation Auslander–Reiten quiver Coxeter–Catalan combinatorics Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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