VALUATED MATROIDS

Oriented matroids have been introduced in [R. G. Bland and M. Las Vergnas, Orientability of Matroids, J. Combin. Theory Ser. B 24 (1978), 94-123]. They can be viewed as an abstraction of matroids representable over an ordered field. Analogously, we define valuated matroids as an abstraction of matroids which are representable over some field having a non-archimedian valuation. We study projective equivalence of valuations of matroids and show that valuated matroids correspond in a one-to-one fashion to matroids with coefficients in certain coefficient domains. © 1992.