Constructions of maximum few-distance sets in euclidean spaces

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Abstract

A finite set of vectors X in the d-dimensional Euclidean space Rd is called an s-distance set if the set of mutual distances between distinct elements of X has cardinality exactly 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 in Rd for d ≤ 8 and s ≤ 6, and independently verify several earlier results from the literature.

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Original languageEnglish
Article numberP1.23
JournalElectronic Journal of Combinatorics
Volume27
Issue number1
Publication statusPublished - 1 Jan 2020
MoE publication typeA1 Journal article-refereed

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