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- W2061865729 abstract "R. B. Kusner [R. Guy, Amer. Math. Monthly 90, 196-199 (1983)] asked whether a set of vectors in $ {mathbb R}^{d} $ such that the $ ell_p $ distance between any pair is 1, has cardinality at most d + 1. We show that this is true for p = 4 and any $ d geq 1 $ , and false for all 1<p<2 with d sufficiently large, depending on p. More generally we show that the maximum cardinality is at most $ (2lceil p/4rceil-1)d+1 $ if p is an even integer, and at least $ (1 + varepsilon_p)d $ if 1<p<2, where $ varepsilon_{p} > 0 $ depends on p." @default.
- W2061865729 created "2016-06-24" @default.
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- W2061865729 date "2004-08-01" @default.
- W2061865729 modified "2023-10-16" @default.
- W2061865729 title "A problem of Kusner on equilateral sets" @default.
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- W2061865729 doi "https://doi.org/10.1007/s00013-003-4840-8" @default.
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