An interpretation for the Tutte polynomial

For any matroid M realizable over Q, we give a combinatorial interpretation of the Tutte polynomial T-M(x, y) which generalizes many of its known interpretations and specializations, including Tune's coloring and flow interpretations of T-M(1 - t, 0), T-M(0, 1 - t): Crape and Rota's finite field interpretation of T-M (1 - q(k), 0); the interpretation in terms of the Whitney corank-nullity polynomial; Greene's interpretation as the weight enumerator of a linear code and its recent generalization to higher weight enumerators by Barg; Jaeger's interpretation in terms of linear code words and dual code words with disjoint support; and Brylawksi and Oxley's two-variable coloring formula. (C) 1999 Academic Press .