Borsuk's Conjecture Fails in Dimensions 321 and 322

Details Borsuk's Conjecture Fails in Dimensions 321 and 322 Borsuk's Conjecture Fails in Dimensions 321 and 322

2002-02-12

arxiv.org/abs/math/0202112v1

Mathematics

Combinatorics

3 pages

Scientific paper

Borsuk's conjecture states that any bounded set in R^n can be partitioned
into n+1 sets of smaller diameter. It is known to be false for all n bigger or
equal to 323.
Here we show that Borsuk's conjecture fails in dimensions 321 and 322. (This
result has been independently discovered by Hinrichs and Richter.)

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