On Matroids Representable over

and other Fields

Author:
Geoff Whittle

Journal:
Trans. Amer. Math. Soc. **349** (1997), 579-603

MSC (1991):
Primary 05B35

DOI:
https://doi.org/10.1090/S0002-9947-97-01893-X

MathSciNet review:
1407504

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Abstract | References | Similar Articles | Additional Information

Abstract: The matroids that are representable over and some other fields depend on the choice of field. This paper gives matrix characterisations of the classes that arise. These characterisations are analogues of the characterisation of regular matroids as the ones that can be represented over the rationals by a totally-unimodular matrix. Some consequences of the theory are as follows. A matroid is representable over and if and only if it is representable over and the rationals, and this holds if and only if it is representable over for all odd primes . A matroid is representable over and the complex numbers if and only if it is representable over and . A matroid is representable over , and if and only if it is representable over every field except possibly . If a matroid is representable over for all odd primes , then it is representable over the rationals.

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Additional Information

**Geoff Whittle**

Affiliation:
Department of Mathematics, Victoria University, PO Box 600 Wellington, New Zealand

Email:
whittle@kauri.vuw.ac.nz

DOI:
https://doi.org/10.1090/S0002-9947-97-01893-X

Received by editor(s):
August 20, 1994

Article copyright:
© Copyright 1997
American Mathematical Society