A Generalisation of Tverberg%26apos;s Theorem

作者：Soberon Pablo; Strausz Ricardo^*

来源：DISCRETE %26 COMPUTATIONAL GEOMETRY, 2012, 47(3): 455-460.

DOI：10.1007/s00454-011-9379-z

• Tverberg partition
• Tolerance

We will prove the following generalisation of Tverberg%26apos;s Theorem: given a set SaS,a%26quot;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).

• 出版日期2012-4