Definition:Rank (Matroid)

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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