A two-page disproof of the Borsuk partition conjecture
Combinatorics
2018-10-02 v3 Metric Geometry
Abstract
It is presented the simplest known disproof of the Borsuk conjecture stating that if a bounded subset of n-dimensional Euclidean space contains more than n points, then the subset can be partitioned into n+1 nonempty parts of smaller diameter. The argument is due to N. Alon and is a remarkable application of combinatorics and algebra to geometry. This note is purely expository and is accessible for students.
Cite
@article{arxiv.0712.4009,
title = {A two-page disproof of the Borsuk partition conjecture},
author = {A. Skopenkov},
journal= {arXiv preprint arXiv:0712.4009},
year = {2018}
}
Comments
3+4 pages, in English and in Russian; minor corrections