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Bibliographic Details
Main Authors: Bárány, Imre, Qi, Yun
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.22907
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Table of Contents:
  • Steinitz's theorem states that if a point $a \in \mathrm{int\,conv\,} X$ for a set $X \subset \mathbb{R}^d$, then $X$ contains a subset $Y$ of size at most $2d$ such that $a \in \mathrm{int\,conv\,}Y$. The bound $2d$ is best possible here. We prove the colourful version of this theorem and characterize the cases when exactly $2d$ sets are needed.