# Plus minus analogues for affine Tverberg type results

## TL;DR

This paper introduces plus minus analogues for affine Tverberg type results, providing new proofs and extending known theorems using projective transformations, including a plus minus version of the optimal colored Tverberg theorem.

## Contribution

It offers a new proof of the Tverberg plus minus theorem and derives plus minus analogues of all known affine Tverberg results using projective transformations.

## Key findings

- New proof of the Tverberg plus minus theorem
- Plus minus analogues of all known affine Tverberg results
- Plus minus version of the optimal colored Tverberg theorem

## Abstract

The classical 1966 theorem of Tverberg with its numerous variations was and still is a motivating force behind many important developments in convex and computational geometry as well as the testing ground for methods from equivariant algebraic topology. In 2018, B\'ar\'any and Sober\'on presented a new variation, the "Tverberg plus minus theorem." In this paper, we give a new proof of the Tverberg plus minus theorem, by using a projective transformation. The same tool allows us to derive plus minus analogues of all known affine Tverberg type results. In particular, we prove a plus minus analogue of the optimal colored Tverberg theorem.