Equilateral sets and a Schütte theorem for the 4-norm

Swanepoel, Konrad J. ORCID: 0000-0002-1668-887X (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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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
Date Deposited:	12 Nov 2014 11:41
Last Modified:	01 Apr 2024 08:22
URI:	http://eprints.lse.ac.uk/id/eprint/60151

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