A note on Tutte’s unimodular representation theorem
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- by Tom Brylawski PDF
- Proc. Amer. Math. Soc. 52 (1975), 499-502 Request permission
Abstract:
A short, direct, and constructive proof is given of a result of W. T. Tutte (Lectures on matroids, J. Res. Nat. Bur. Standards Sect. B 69B (1965), 1-47). Theorem. Let $G$ be an abstract finite combinatorial geometry whose dependencies can be represented by vectors over the field with two elements as well as by vectors over another field of characteristic other than two. Then $G$ may be represented simultaneously over every field by the column vectors of a totally unimodular matrix.References
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T. H. Brylawski and T. D. Lucas, Uniquely representable combinatorial geometries, Proc. Internat. Colloq. Combinatorial Theory, Rome, Italy 1975.
- Paul Camion, Characterization of totally unimodular matrices, Proc. Amer. Math. Soc. 16 (1965), 1068–1073. MR 180568, DOI 10.1090/S0002-9939-1965-0180568-2
- W. T. Tutte, Lectures on matroids, J. Res. Nat. Bur. Standards Sect. B 69B (1965), 1–47. MR 179781, DOI 10.6028/jres.069B.001
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 499-502
- MSC: Primary 05B35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0419271-6
- MathSciNet review: 0419271