On the Geometry of Holmsen's Combinatorial Version of the Colorful Carath\'eodory
Combinatorics
2019-04-29 v1
Abstract
Carath\'eodorys Theorem of convex hulls plays an important role in convex geometry. In 1982, B\'ar\'any formulated and proved a more general version, called the Colorful Carath\'eodory. This colorful version was even more generalized by Holmsen in 2016. He formulated a combinatorial extension and found a topological proof. Taking a dual point of view we gain an equivalent formulation of Holmsen's result that has a more geometric meaning.
Keywords
Cite
@article{arxiv.1904.11698,
title = {On the Geometry of Holmsen's Combinatorial Version of the Colorful Carath\'eodory},
author = {Helena Bergold and Winfried Hochstättler},
journal= {arXiv preprint arXiv:1904.11698},
year = {2019}
}