An interpretation for the Tutte polynomial

Victor Reiner

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 languageEnglish (US)
Pages (from-to)149-161
Number of pages13
JournalEuropean Journal of Combinatorics
Volume20
Issue number2
DOIs
StatePublished - Feb 1999

Bibliographical note

Funding Information:
†Supported by Sloan Foundation and University of Minnesota McKnight-Land Grant Fellowships.

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