Complete positivity and distance-avoiding sets

Journal article (2020)

Authors

Evan DeCorte McGill University
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS
Frank Vallentin Universität zu Köln
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2020 Evan DeCorte, F.M. de Oliveira Filho, Frank Vallentin
DOI: https://doi.org/10.1007/s10107-020-01562-6
More Info
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Published Date

2020

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

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.