An Interpretation for the Tutte Polynomial

Author: Reiner V.

Source: European Journal of Combinatorics, Volume 20, Number 2, February 1999 , pp. 149-161(13)

Publisher: Academic Press

Abstract:

For any matroid M realizable over , we give a combinatorial interpretation of the Tutte polynomial T_M(x,y) which generalizes many of its known interpretations and specializations, including Tutte's coloring and flow interpretations of T_M(1 - t ,0), T_M(0, - t); Crapo 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. Copyright 1999 Academic Press

Language: English

Document Type: Research article

Affiliations: School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, U.S.A.

Publication date: 1999-02-01

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