A Generalisation of Tverberg's Theorem
We will prove the following generalisation of Tverberg's Theorem: given a set SaS,a"e (d) of (r+1)(k-1)(d+1)+1 points, there is a partition of S in k sets A (1),A (2),aEuro broken vertical bar,A (k) such that for any CaS,S of at most r points, the convex hulls of A (1)\C,A (2)\C,aEuro broken vertical bar,A (k) \C are intersecting. This was conjectured first by Natalia Garcia-Colin (Ph.D. thesis, University College of London, 2007).
tverberg partition tolerance