A Generalisation of Tverberg's Theorem.

We will prove the following generalisation of Tverberg's Theorem: given a set S⊂ℝ of ( r+1)( k−1)( d+1)+1 points, there is a partition of S in k sets A, A,..., A such that for any C⊂ S of at most r points, the convex hulls of A\ C, A\ C,..., A\ C are intersecting. This was conjectured first by Natalia García-Colín (Ph.D. thesis, University College of London, ). [ABSTRACT FROM AUTHOR]