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Title: On complete classes of valuated matroids

Abstract:

Valuated matroids were introduced by Dress and Wenzel in 1992. They are a central object in discrete convex analysis, and play important roles in other areas such as mathematical economics and tropical geometry. Finding a constructive characterization, i.e., showing that all valuated matroids can be derived from a simple class by some basic operations has been a natural question proposed in various contexts.