arXiv:1505.04952 Abstract | arXiv Analytics

arXiv:1505.04952 [math.CO]Abstract References Reviews Resources

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

Published 2015-05-19Version 1

Borsuk asked in 1933 if every set of diameter 1 in $R^d$ 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.

Comments: This is a draft of a chapter for "Surveys in Combinatorics 2015," edited by Artur Czumaj, Angelos Georgakopoulos, Daniel Kral, Vadim Lozin, and Oleg Pikhurko. The final published version shall be available for purchase from Cambridge University Press

Categories: math.CO, cs.CG, math.MG

Keywords: borsuks problem, combinatorial geometry, smaller diameter, negative solution

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