2025/12/28 by Bárány, Imre, Qi, Yun
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.22907
Steinitz's theorem states that if a point a ∈ int conv X for a set X ⊂ ℝd, then X contains a subset Y of size at most 2d such that a ∈ 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.