Oriented matroids and associated valuations

Abstract

It is possible to associate a valuation on the "orthant lattice" with each oriented matroid. In the case of uniform oriented matroids, it is not difficult to provide a characterization of the corresponding valuations. This is done here, thereby establishing a new characterization of the uniform oriented matroids themselves. Additionally, the connection between the valuations and the total polynomials associated with uniform oriented matroids is noted. © 2004 Springer-Verlag New York, LLC.