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Constructions of maximum few-distance sets in euclidean spaces
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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18
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Electronic Journal of Combinatorics, Volume 27, issue 1
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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Östergård, P R J & Szollosi, F 2020, 'Constructions of maximum few-distance sets in euclidean spaces', Electronic Journal of Combinatorics, vol. 27, no. 1, P1.23. https://doi.org/10.37236/8565