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

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

## 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 |
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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: | 20 Jun 2022 10:45 |

URI: | http://eprints.lse.ac.uk/id/eprint/108659 |

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