The density of sets avoiding distance 1 in Euclidean space
Langue
en
Document de travail - Pré-publication
Résumé en anglais
We improve by an exponential factor the best known asymptotic upper bound for the density of sets avoiding 1 in Euclidean space. This result is obtained by a combination of an analytic bound that is an analogue of Lovasz ...Lire la suite >
We improve by an exponential factor the best known asymptotic upper bound for the density of sets avoiding 1 in Euclidean space. This result is obtained by a combination of an analytic bound that is an analogue of Lovasz theta number and of a combinatorial argument involving finite subgraphs of the unit distance graph. In turn, we straightforwardly obtain an asymptotic improvement for the measurable chromatic number of Euclidean space. We also tighten previous results for the dimensions between 4 and 24.< Réduire
Mots clés en anglais
unit distance graph
measurable chromatic number
theta number
linear programming
Origine
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