Definition:Free Matroid

Definition

Let $S$ be a finite set.

Let $\mathscr I = \powerset S$ be the power set of $S$.

That is, let $\mathscr I$ be the set of all subsets of $S$:

$\mathscr I := \set {X: X \subseteq S}$

Then the ordered pair $\struct{S, \mathscr I}$ is called the free matroid of $S$.

Also see

• Free Matroid is Matroid

Sources

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