Kirchberger's Theorem for Complexes of Oriented Matroids
Combinatorics
2022-07-29 v2
Abstract
The separation theorem of Kirchberger can be proven using a combination of Farkas' Lemma and Caratheodory's Theorem. Since those theorems are at the heart of oriented matroids, we are interested in a generalization of Kirchberger's Theorem to them. This has already been done for rank 3 oriented matroids. Here we prove it for complexes of oriented matroids, which are a generalization of oriented matroids.
Cite
@article{arxiv.2112.03589,
title = {Kirchberger's Theorem for Complexes of Oriented Matroids},
author = {Winfried Hochstättler and Sophia Keip and Kolja Knauer},
journal= {arXiv preprint arXiv:2112.03589},
year = {2022}
}
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7 Pages