Span (Matroid)

Definition

Span (Matroid)

Given a matroid $\mathcal{M}=(E,\mathcal{I})$ and a subset $X\subseteq E$, the span of $X$ is defined as

$$\mathrm{span}(X)=X\cup \{e\in E\setminus X:\mathrm{rank}(X\cup \{e\})=\mathrm{rank}(X)\}.$$