Large equilateral sets in subspaces of ℓ∞n of small codimension

Frankl, Nora (2022) Large equilateral sets in subspaces of ℓ∞n of small codimension. Discrete and Computational Geometry, 67 (3). 882 - 893. ISSN 0179-5376

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Abstract

For fixed k we prove exponential lower bounds on the equilateral number of subspaces of ℓ∞n of codimension k. In particular, we show that subspaces of codimension 2 of ℓ∞n+2 and subspaces of codimension 3 of ℓ∞n+3 have an equilateral set of cardinality n+ 1 if n≥ 7 and n≥ 12 respectively. Moreover, the same is true for every normed space of dimension n, whose unit ball is a centrally symmetric polytope with at most 4 n/ 3 - o(n) pairs of facets.

Item Type:	Article
Official URL:	https://www.springer.com/journal/454
Additional Information:	© 2021 The Author
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	15 Feb 2021 08:54
Last Modified:	12 Dec 2024 02:26
URI:	http://eprints.lse.ac.uk/id/eprint/108659

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