Definition:Rank (Matroid)

Definition

Let $M = \struct{S, \mathscr I}$ be a matroid.

Let $\rho : \powerset S \to \Z$ be the rank function of $M$.

The rank of $M$, denoted by $\map \rho M$, is the image of $S$ under $\rho$, that is:

$\map \rho M = \map \rho S$.

Sources

• 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 2.$ Axiom Systems for a Matroid