Tverberg’s theorem, a new proof

Bárány, Imre (2024) Tverberg’s theorem, a new proof. ISRAEL JOURNAL OF MATHEMATICS, accept. ISSN 0021-2172

Preview

Text 2308.10105v1.pdf Available under License Creative Commons Attribution. Download (122kB) | Preview

Abstract

We give a new proof Tverberg’s famous theorem: For every set X ⊂ Rd with |X| = (r − 1)(d + 1) + 1, there is a partition of X into r sets X1, ... , Xr such that ⋂r p=1 convXp 6 = ∅. The new proof uses linear algebra, specially structured matrices, the theory of linear equations, and Tverberg’s original “moving the points” method.

Actions (login required)

Edit Item