An infinite family of minor-minimal nonrealizable 3-chirotopes (Q1102974)
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scientific article; zbMATH DE number 4051649
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An infinite family of minor-minimal nonrealizable 3-chirotopes |
scientific article; zbMATH DE number 4051649 |
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An infinite family of minor-minimal nonrealizable 3-chirotopes (English)
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1989
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A result of \textit{P. Vamos}, ``The missing (local) axiom of matroid theory is lost for ever'' [J. Lond. Math. Soc., II. Ser. 18, 403-408 (1978; Zbl 0395.05024)] will be proved to hold for oriented maroids or chirotopes, too. We construct an infinite family of minor-minimal nonrealizable simplicial 3-chirotopes. This family and its properties play a substantial role in a recent contribution of the second author to the Steinitz-problem in higher dimensions.
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oriented matroids
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chirotopes
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Steinitz-problem in higher dimensions
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