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

Journal article (2019)

Authors

F.M. Filho Discrete Mathematics and Optimization
Frank Vallentin University of Cologne
Research Group
Discrete Mathematics and Optimization
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Published Date

2019

Language

English

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Research Group

Discrete Mathematics and Optimization

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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