Library Header Image
LSE Research Online LSE Library Services

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). pp. 882-893. ISSN 0179-5376

Full text not available from this repository.

Identification Number: 10.1007/s00454-020-00272-2


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:
Additional Information: © 2021 The Author
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 15 Feb 2021 08:54
Last Modified: 20 Jun 2022 10:45

Actions (login required)

View Item View Item