An elementary proof of Sierksma's conjecture for seven points in the plane
Combinatorics
2026-04-21 v1
Abstract
We give a new simple geometric proof that any seven points in the plane have four Tverberg partitions into three sets. This is the only confirmed non-trivial case of Sierksma's conjecture. Earlier proofs, by Stephan Hell, relied on topological arguments.
Cite
@article{arxiv.2604.18485,
title = {An elementary proof of Sierksma's conjecture for seven points in the plane},
author = {Pablo Soberón},
journal= {arXiv preprint arXiv:2604.18485},
year = {2026}
}
Comments
5 pages, 2 figures