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

Fernando Mário de Oliveira Filho; Frank Vallentin

doi:10.1112/S0025579319000160

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

Fernando Mário de Oliveira Filho, Frank Vallentin

Optimization

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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.

Original language	English
Pages (from-to)	785-787
Number of pages	3
Journal	Mathematika
Volume	65
Issue number	3
DOIs	https://doi.org/10.1112/S0025579319000160
Publication status	Published - 2019

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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.",

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

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