Category:Circuits of Matroid iff Matroid Circuit Axioms

This category contains pages concerning Circuits of Matroid iff Matroid Circuit Axioms:

Let $S$ be a finite set.

Let $\mathscr C$ be a non-empty set of subsets of $S$.

Then:

$\mathscr C$ is the set of circuits of a matroid on $S$

if and only if

$\mathscr C$ satisfies the circuit axioms