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.
|Julkaisu||Electronic Journal of Combinatorics|
|DOI - pysyväislinkit|
|Tila||Julkaistu - 24 tammik. 2020|
|OKM-julkaisutyyppi||A1 Julkaistu artikkeli, soviteltu|