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Equilateral sets and a Schütte theorem for the 4-norm

Swanepoel, Konrad J. (2014) Equilateral sets and a Schütte theorem for the 4-norm. Canadian Mathematical Bulletin, 57 (3). pp. 640-647. ISSN 0008-4395

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Identification Number: 10.4153/CMB-2013-031-0

Abstract

A well-known 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 .

Item Type: Article
Official URL: http://cms.math.ca/cmb/
Additional Information: © 2014 Canadian Mathematical Society
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 12 Nov 2014 11:41
Last Modified: 20 Feb 2019 11:00
URI: http://eprints.lse.ac.uk/id/eprint/60151

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