Matroid: basis

Dependencies:

1. Matroid

Let $M = (S, I)$ be a matroid and let $X \subseteq S$. Then $B$ is a basis of $X$ iff both these conditions hold:

• Independence: $B \in I$.
• Maximality: $\forall x \in X-B, B + x \not\in I$.

When $X = S$, we say that $B$ is a basis of $M$.

The plural of 'basis' is 'bases'. 'Base' is a synonym for basis.

Dependency for:

1. Matroid: rank of set increment
2. Matroid: basis iff size is rank
3. Matroid: basis of set increment
4. Matroid: expanding to basis

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Matroid