English

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.

Keywords

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}
}

Comments

7 Pages

R2 v1 2026-06-24T08:07:17.611Z