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Designs and Matroids

Authored by: Peter J. Cameron , Michel M. Deza

Handbook of Combinatorial Designs

Print publication date:  November  2006
Online publication date:  November  2006

Print ISBN: 9781584885061
eBook ISBN: 9781420010541
Adobe ISBN:

10.1201/9781420010541-109

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Abstract

10.1

A matroid is a pair ( E ,   I ) where E is a set and I a nonempty family of subsets of E (independent sets) satisfying the conditions:

if I ∈ I and J ⊆ I, then J ∈ I

(the Exchange Axiom) if I 1 ,   I 2 ∈ I and |I 2| > |I 2|, then there exists e ∈ I 2 \I 1 such that I 1 ∪ { e } 2 ∈ I .

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