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A counterexample to Borsuk's conjecture


Authors: Jeff Kahn and Gil Kalai
Journal: Bull. Amer. Math. Soc. 29 (1993), 60-62
MSC (2000): Primary 52A20
DOI: https://doi.org/10.1090/S0273-0979-1993-00398-7
MathSciNet review: 1193538
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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) \geq (1.2)\sqrt d $ for large d.


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DOI: https://doi.org/10.1090/S0273-0979-1993-00398-7
Article copyright: © Copyright 1993 American Mathematical Society