Some old and new problems in combinatorial geometry I: Around Borsuk's problem
Combinatorics
2015-05-20 v1 Computational Geometry
Metric Geometry
Abstract
Borsuk asked in 1933 if every set of diameter 1 in can be covered by 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.
Cite
@article{arxiv.1505.04952,
title = {Some old and new problems in combinatorial geometry I: Around Borsuk's problem},
author = {Gil Kalai},
journal= {arXiv preprint arXiv:1505.04952},
year = {2015}
}
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