Uniform matroid
= Uniform matroid
{title2=$U_{r,n}$}
For $0\leq r\leq n$, the <uniform matroid> $U_{r,n}$ on an $n$-element <ground set> has as its <matroid independent sets> exactly the <subsets> of <cardinality> at most $r$. Heredity is immediate, and augmentation works because any smaller such <subset> can acquire an element of a larger one without exceeding $r$. Its <rank of a matroid> on $A$ is $\min\{|A|,r\}$.