Abstract
For any matroid M realizable over ℚ, we give a combinatorial interpretation of the Tutte polynomial TM(x, y) which generalizes many of its known interpretations and specializations, including Tutte's coloring and flow interpretations of TM(1 - t, 0), TM(0, 1 - t); Crapo and Rota's finite field interpretation of TM (1 - qk, 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.
Original language | English (US) |
---|---|
Pages (from-to) | 149-161 |
Number of pages | 13 |
Journal | European Journal of Combinatorics |
Volume | 20 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1999 |
Bibliographical note
Funding Information:†Supported by Sloan Foundation and University of Minnesota McKnight-Land Grant Fellowships.