Odd-Distance Sets and Right-Equidistant Sequences in the Maximum and Manhattan Metrics

We solve two related extremal-geometric questions in the n -dimensional space equipped with the maximum metric. First, we prove that the maximum size of a right-equidistant sequence of points in equals . A sequence is right-equidistant if each of the points is at the same distance from all the succe...

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Bibliographic Details
Published inDoklady. Mathematics Vol. 106; no. 2; pp. 340 - 342
Main Authors Golovanov, A. I., Kupavskii, A. B., Sagdeev, A. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.11.2022
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Questions
maximum metric
equilateral dimension
odd-distance sets
Manhattan metric
right-equidistant sequences
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Summary:We solve two related extremal-geometric questions in the n -dimensional space equipped with the maximum metric. First, we prove that the maximum size of a right-equidistant sequence of points in equals . A sequence is right-equidistant if each of the points is at the same distance from all the succeeding points. Second, we prove that the maximum number of points in with pairwise odd distances equals 2 n . We also obtain partial results for both questions in the n -dimensional space with the Manhattan distance.
ISSN:1064-5624
1531-8362
DOI:10.1134/S106456242205012X