Chessboard complexes indomitable

TL;DR

This paper provides an alternative proof of a Tverberg-type theorem, introduces new constrained Tverberg cases, and presents a simple colored Radon's theorem, advancing combinatorial geometry understanding.

Contribution

It offers a new proof method for a Tverberg theorem and extends results to new constrained cases, including a simple colored Radon's theorem.

Findings

Alternative proof of a Tverberg-type theorem

New constrained Tverberg cases in geometric combinatorics

A simple colored Radon's theorem for d+3 points in R^d

Abstract

We give an alternative proof of the striking new Tverberg type theorem of Blagojevic and Ziegler, arXiv:0910.4987v1 [math.CO]. Our method also yields some new cases of "constrained Tverberg thereom" in the sense of Hell, including a simple colored Radon's theorem for d+3 points in R^d. This is a final version of the paper with improved presentation, corrected typos and added references.