On Circuit Valuation of Matroids 1
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چکیده
The concept of valuated matroids was introduced by Dress and Wenzel as a quantitative extension of the base exchange axiom for matroids. This paper gives several sets of cryptomorphically equivalent axioms of valuated matroids in terms of (R[f 1g)-valued vectors de ned on the circuits of the underlying matroid, where R is a totally ordered additive group. The dual of a valuated matroid is characterized by an orthogonality of (R [ f 1g)valued vectors on circuits. Minty's characterization for matroids by the painting property is generalized for valuated matroids.
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تاریخ انتشار 2000