Another simple proof of Kirchberger's theorem

Webster, Roger

doi:10.1016/0022-247x(83)90286-x

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2024

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Cited by 3 publications

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“…One possibility is to prove it using Helly's Theorem like in [2] or [8]. There is also a simpler proof which is basically a combination of Carathéodory's Theorem and Farkas' Lemma which can be found in [10]. Because those two theorems are crucial for oriented matroids (OMs), it is natural to generalize Kirchberger's Theorem to them as well.…”

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confidence: 99%

Kirchberger's Theorem for Complexes of Oriented Matroids

Hochstättler¹,

Keip²,

Knauer³

2021

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The separation theorem of Kirchberger can be proven using a combination of Farkas' Lemma and Carathéodory'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.

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confidence: 99%