= Small matroid enumeration
On labelled <ground sets> of sizes $1,2,3$, there are respectively $2,5,16$ <matroids>, or $2,4,8$ up to <matroid isomorphism>. At <rank of a matroid> one, a nonempty <subset> of <nonloops> specifies all <matroid independent sets> of <cardinality> one. On three labels at <rank of a matroid> two, the three types are one <matroid loop> with an independent pair, no <matroid loops> with one pair of <parallel elements of a matroid>, and all pairs independent with the triple dependent.
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