Definition:Rank Function (Matroid)
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Definition
Let $M = \struct {S, \mathscr I}$ be a matroid.
The rank function of $M$ is the mapping $\rho : \powerset S \to \Z$ from the power set of $S$ into the integers defined by:
- $\forall A \subseteq S : \map \rho A = \max \set {\size X : X \subseteq A \land X \in \mathscr I}$
where $\size A$ denotes the cardinality of $A$.
Sources
- 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 2.$ Axiom Systems for a Matroid