184 research outputs found
Dissections, Hom-complexes and the Cayley trick
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.Comment: 23 pages, 5 figures; improved exposition; accepted for publication in
JCT
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