Affiliation:
1. West Virginia University Morgantown West Virginia USA
Abstract
AbstractLet be the hypercube of dimension and let and be subsets of the vertex set , called configurations in . We say that is an exact copy of if there is an automorphism of which sends onto . Let be an integer, let be a configuration in and let be a configuration in . We let be the maximum, over all configurations in , of the fraction of sub‐‐cubes of in which is an exact copy of , and we define the ‐cube density of to be the limit as goes to infinity of . We determine for several configurations in and as well as for an infinite family of configurations. There are strong connections with the inducibility of graphs.
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics
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