A counterexample to Borsuk’s conjecture

Jeff Kahn; Gil Kalai

doi:10.1090/S0273-0979-1993-00398-7

A counterexample to Borsuk’s conjecture

Jeff Kahn
, Gil Kalai

Einstein Institute of Mathematics

Research output: Contribution to journal › Comment/debate

144 Scopus citations

Abstract

Let f(d) be the smallest number so that every set in R^d of diameter 1 can be partitioned into f(d) sets of diameter smaller than 1. Borsuk’s conjecture was that f(d) = d+1. We prove that f(d) ≥ (1.2)(Equation presented) for large d.

Original language	English
Pages (from-to)	60-62
Number of pages	3
Journal	Bulletin of the American Mathematical Society
Volume	29
Issue number	1
DOIs	https://doi.org/10.1090/S0273-0979-1993-00398-7
State	Published - Jul 1993

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abstract = "Let f(d) be the smallest number so that every set in Rd of diameter 1 can be partitioned into f(d) sets of diameter smaller than 1. Borsuk{\textquoteright}s conjecture was that f(d) = d+1. We prove that f(d) ≥ (1.2)(Equation presented) for large d.",

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AB - Let f(d) be the smallest number so that every set in Rd of diameter 1 can be partitioned into f(d) sets of diameter smaller than 1. Borsuk’s conjecture was that f(d) = d+1. We prove that f(d) ≥ (1.2)(Equation presented) for large d.

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A counterexample to Borsuk’s conjecture

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