On exchange properties for Coxeter matroids and oriented matroids (Q1377708)
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scientific article; zbMATH DE number 1109982
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On exchange properties for Coxeter matroids and oriented matroids |
scientific article; zbMATH DE number 1109982 |
Statements
On exchange properties for Coxeter matroids and oriented matroids (English)
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29 May 1998
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New axiom systems are presented for the basis systems of matroids, of oriented matroids, and Coxeter matroids (formerly known as WP-matroids). This includes an ``increasing exchange property'' which characterizes Coxeter matroids. Other equivalent axioms for matroid bases turn out to be weaker in the Coxeter matroid setting. A weakened characterization of chirotopes (basis orientations of oriented matroids) is also obtained.
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axiom systems for bases
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matroids
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oriented matroids
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WP-matroids
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Coxeter matroids
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root systems
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matroid polytopes
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