A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1

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A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1

Journal Article (2019)

Author(s)

Fernando Mário de Oliveira Filho (TU Delft - Discrete Mathematics and Optimization)

Frank Vallentin (Universität zu Köln)

DOI related publication

https://doi.org/10.1112/S0025579319000160 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:62fbc425-c656-4eb3-b6e8-7ddf7ced8c8f

More Info

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Publication Year

2019

Language

English

Journal title

Mathematika

Issue number

3

Volume number

65

Pages (from-to)

785-787

Downloads counter

186

Abstract

For each (Formula presented.) we construct a measurable subset of the unit ball in (Formula presented.) that does not contain pairs of points at distance 1 and whose volume is greater than (Formula presented.) times the volume of the unit ball. This disproves a conjecture of Larman and Rogers from 1972.