Matroid representation over GF(3)

P. D. Seymour

doi:10.1016/0095-8956(79)90055-8

Matroid representation over GF(3)

P. D. Seymour

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	159-173
Number of pages	15
Journal	Journal of Combinatorial Theory, Series B
Volume	26
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(79)90055-8
State	Published - Apr 1979
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(79)90055-8

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AB - 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.

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Matroid representation over GF(3)

Abstract

All Science Journal Classification (ASJC) codes

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