Free matroid

Summary

In mathematics, the free matroid over a given ground-set $E$ is the matroid in which the independent sets are all subsets of $E$. It is a special case of a uniform matroid; specifically, when $E$ has cardinality $n$, it is the uniform matroid $U{}^{n}_{n}$. The unique basis of this matroid is the ground-set itself, $E$. Among matroids on $E$, the free matroid on $E$ has the most independent sets, the highest rank, and the fewest circuits.