English

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.

Keywords

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