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Borsuk's Conjecture Fails in Dimensions 321 and 322

Combinatorics 2007-05-23 v1

Abstract

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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Cite

@article{arxiv.math/0202112,
  title  = {Borsuk's Conjecture Fails in Dimensions 321 and 322},
  author = {Oleg Pikhurko},
  journal= {arXiv preprint arXiv:math/0202112},
  year   = {2007}
}

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3 pages