On Borsuk's conjecture for twodistance sets
Abstract
In this paper we answer Larman's question on Borsuk's conjecture for twodistance sets. We find a twodistance set consisting of 416 points on the unit sphere in the dimension 65 which cannot be partitioned into 83 parts of smaller diameter. This also reduces the smallest dimension in which Borsuk's conjecture is known to be false. Other examples of twodistance sets with large Borsuk's numbers will be given.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 arXiv:
 arXiv:1305.2584
 Bibcode:
 2013arXiv1305.2584B
 Keywords:

 Mathematics  Metric Geometry;
 05C50;
 52C35;
 41A55;
 41A63
 EPrint:
 9 pages