Swanepoel, Konrad J.
(2014)
Equilateral sets and a Schütte theorem for the 4norm.
Canadian Mathematical Bulletin, 57 (3).
pp. 640647.
ISSN 00084395
Abstract
A wellknown theorem of Schütte (1963) gives a sharp lower bound for the ratio of the maximum and minimum distances between n+2 points in n dimensional Euclidean space. In this note we adapt Bárány's elegant proof (1994) of this theorem to the space ℓ n 4 . This gives a new proof that the largest cardinality of an equilateral set in ℓ n 4 is n+1 , and gives a constructive bound for an interval (4−ε n ,4+ε n ) of values of p close to 4 for which it is known that the largest cardinality of an equilateral set in ℓ n p is n+1 .
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