On exchange properties for Coxeter matroids and oriented matroids
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.
scientific article; zbMATH DE number 1109982
scientific article