Definition:Uniform Matroid

Definition
Let $S$ be a finite set of cardinality $n$.

Let $\mathscr I_{k,n}$ be the set of all subsets of $S$ of cardinality less than or equal to $k$.

Then the ordered pair $\struct{S, \mathscr I_{k,n}}$ is called the uniform matroid of rank $k$ and is denoted $U_{k,n}$.

Also see

 * Uniform Matroid is Matroid