Complete positivity and distance-avoiding sets
Evan DeCorte (McGill University)
Fernando Mário Filho (TU Delft - Discrete Mathematics and Optimization)
Frank Vallentin (Universität zu Köln)
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Abstract
We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space.
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