On the number of colored Birch and Tverberg partitions

TL;DR

This paper extends the colored Tverberg theorem by establishing evenness and lower bounds on the number of colored Tverberg and Birch partitions, advancing understanding of their combinatorial properties.

Contribution

It introduces a colored version of previous results, providing new lower bounds and evenness properties for colored Tverberg and Birch partitions.

Findings

Established evenness of the number of colored Tverberg partitions

Derived non-trivial lower bounds for the count of colored Tverberg partitions

Extended results from uncolored to colored partitions

Abstract

In 2009, Blagojevic, Matschke & Ziegler established the first tight colored Tverberg theorem, but no lower bounds for the number of colored Tverberg partitions. We develop a colored version of our previous results (2008), and we extend our results from the uncolored version: Evenness and non-trivial lower bounds for the number of colored Tverberg partitions. This follows from similar results on the number of colored Birch partitions.