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A note on Tutte's unimodular representation theorem


Author: Tom Brylawski
Journal: Proc. Amer. Math. Soc. 52 (1975), 499-502
MSC: Primary 05B35
MathSciNet review: 0419271
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0419271-6
Keywords: Chain group, combinatorial geometry, dependence geometry, regular matroid, unimodular geometry, coordinatization, matrix, matroid, totally unimodular matrix
Article copyright: © Copyright 1975 American Mathematical Society