A two-page disproof of the Borsuk partition conjecture

Details A two-page disproof of the Borsuk partition conjecture A two-page disproof of the Borsuk partition conjecture

2007-12-24

arxiv.org/abs/0712.4009v2

Mathematics

Combinatorics

3+3 pages, in English and in Russian; exposition simplified

Scientific paper

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.

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