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Some old and new problems in combinatorial geometry I: Around Borsuk's problem

Some old and new problems in combinatorial geometry I: Around Borsuk's problem
Authors: Gil Kalai Download: PDF Abstract: Borsuk asked in 1933 if every set of diameter 1 in $Rd$ can be covered by $d+1$ sets of smaller diameter. In 1993, a negative solution, based on a theorem by Frankl and Wilson, was given by Kahn and Kalai. In this paper I will present questions related to Borsuk's problem.
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