Matroid representation over GF(3)

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We show that a matroid is representable over GF(3) if and only if no minor is the five-point line or the Fano matroid, or their duals. Tutte's famous characterization of the regular matroids is a corollary. A key lemma states that two representations of the same matroid in the same vector space over GF(3) may be transformed one into the other by inverting some points through the origin and taking a linear transformation; no result of this kind holds in larger fields.

Original languageEnglish (US)
Pages (from-to)159-173
Number of pages15
JournalJournal of Combinatorial Theory, Series B
Issue number2
StatePublished - Apr 1979
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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