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Dissections, Hom-complexes and the Cayley trick
Pfeifle, Julián
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. Matemàtica Discreta
We show that certain canonical realizations of the complexes $\Hom(G,H)$ and $\Hom_+(G,H)$ of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For $G$~a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of such projected $\Hom$-complexes: the dissections of a convex polygon into $k$-gons, Postnikov's generalized permutohedra, staircase triangulations, the complex dual to the lower faces of a cyclic polytope, and the graph of weak compositions of an integer into a fixed number of summands.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
Discrete geometry
Polytopes
Cayley trick
Polygon dissection
polytopal complex
clique number
Geometria combinatòria
Geometria discreta
Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
Attribution-NonCommercial-ShareAlike 2.5 Spain
http://creativecommons.org/licenses/by-nc-sa/2.5/es/
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