Constructions of maximum few-distance sets in Euclidean spaces

2018/04/17 by Szöllősi, Ferenc, Östergård, Patric R. J. · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1804.06040

Abstract

A finite set of distinct vectors X in the d-dimensional Euclidean space ℝ^d is called an s-distance set if the set of mutual distances between distinct elements of X has cardinality s. In this paper we present a combined approach of isomorph-free exhaustive generation of graphs and Gröbner basis computation to classify the largest 3-distance sets in ℝ⁴, the largest 4-distance sets in ℝ³, and the largest 6-distance sets in ℝ². We also construct new examples of large s-distance sets for d≤ 8 and s≤ 6, and independently verify several earlier results from the literature.

Cited by

• Constructions of Large m-Distance Sets on Triangular Lattice

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