Associahedra Via Spines
نویسندگان
چکیده
منابع مشابه
Associahedra via Spines
An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree to...
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We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties of these fans then become easy consequences of the known facts about tilting modules due to K. Bongartz, D. Happel and C. M. Ringel.
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We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite types. For the latter, the brick polytopes turn out to coincide with the known realizations of generalized associahedra, thus opening new perspec...
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Spines T a tree on a signed ground set V = V− t V. Spine on T = directed and labeled tree S such that • the labels of the nodes of S form a partition of the signed ground set V, • at a node labeled by U = U− t U, the source label sets of the incoming arcs are subsets of distinct connected components of TrU−, and the sink label sets of the outgoing arcs are subsets of distinct connected componen...
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Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin, and A. Zelevinsky associated to each finite type root system a simple convex polytope, called generalized associahedron. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variab...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2018
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-015-3248-y