| Títol: | Dissections, Hom-complexes and the Cayley trick |
| Autor: | Pfeifle, Julián |
| Altres autors/autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
| Matèries: | 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 |
| Tipus de document: | Article |
| Descripció: | 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. |
| Altres identificadors i accés: | http://hdl.handle.net/2117/433 |
| Disponible al dipòsit: | E-prints UPC
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