Tag Archives: Helly type theorems

Colorful Caratheodory Revisited

Posted on March 15, 2009 by

  Janos Pach wrote me:   ”I saw that you several times returned to the colored Caratheodory and Helly theorems and related stuff, so I thought that you may be interested in the enclosed paper by Holmsen, Tverberg and me, in … Continue reading →

Posted in Convexity | Tagged | 2 Comments

Sarkaria’s Proof of Tverberg’s Theorem 1

Posted on November 24, 2008 by

Helge Tverberg Ladies and gentlemen, this is an excellent time to tell you about the beautiful theorem of Tverberg and the startling proof of Sarkaria to Tverberg’s theorem (two parts). A good place to start is Radon’s theorem.   1. The theorems of … Continue reading →

Posted in Convexity | Tagged , | 13 Comments

Helly’s Theorem, “Hypertrees”, and Strange Enumeration II: The Formula

Posted on June 18, 2008 by

In the first part of this post we discussed an appealing conjecture regaring an extension of Cayley’s counting trees formula. The number of d-dimensional “hypertrees” should somehow add up  to . But it was not clear to us which complexes we want … Continue reading →

Posted in Combinatorics, Convexity | Tagged , , | 2 Comments