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Matroid Theory$
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James Oxley

Print publication date: 2011

Print ISBN-13: 9780198566946

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198566946.001.0001

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Binary Matroids

Binary Matroids

(p.344) 9 Binary Matroids
Matroid Theory

James Oxley

Oxford University Press

This chapter discusses the properties of binary matroids. In particular, it proves numerous characterizations of such matroids. It looks at two vector spaces which are commonly associated with a binary matroid. It extends these ideas to a more general class of matroids and touches briefly on Tutte's theory of chain-groups. It shows how 3-sum for graphs can be extended to binary matroids. It concludes with a discussion of several other special properties of binary matroids.

Keywords:   binary matroids, 3-sum, Tutte's theory of chain groups

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