Definition:Uniform Matroid

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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 $U_{k,n}$.

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