Definition:Rank Function
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Rank Function may refer to:
- Relation Theory:
- Rank Function on a relational structure $\struct {S, \RR}$: a mapping $\operatorname {rk}$ from $S$ to a well-ordered set $\struct {T, \prec}$ such that:
- $\forall x, y \in S: \paren {x \ne y \text { and } \tuple {x, y} \in \RR} \implies \map {\operatorname {rk} } x \prec \map {\operatorname {rk} } y$
- Matroid theory:
- Rank Function of a matroid $M = \struct {S, \mathscr I}$: the mapping from the power set of $S$ into the integers defined by:
- $\forall A \subseteq S : \map \rho A = \max \set {\size X : X \subseteq A \land X \in \mathscr I}$