Let E = {e1, e2, ...em} be a

finite set, and let F be a

family of

subsets
of E: then F is a

matroid if it satisfies

- {ei} in F for each i,

- if G is in F, and if H is a non-empty subset of G, then H is in F.

- for each S that is a subset of E, if G and H are two members of F contained
in S and maximal with this property, then |G|=|H|.

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