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

Sources

• 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1$. $\S 3$. Examples of Matroids