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arXiv · 1804.09099

Complete positivity and distance-avoiding sets

Evan DeCorte·Fernando Mário de Oliveira Filho·Frank Vallentin
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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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Evan DeCorte, Fernando Mário de Oliveira Filho, Frank Vallentin. 2018-04-24. Complete positivity and distance-avoiding sets. https://doi.org/10.1007/s10107-020-01562-6

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