Category:Matroid Rank Functions

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This category contains results about Matroid Rank Functions.

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 $A$.

Subcategories

This category has the following 3 subcategories, out of 3 total.

E

Equivalence of Definitions of Matroid Rank Axioms‎ (3 P)

F

Formulation 1 Rank Axioms Implies Rank Function of Matroid‎ (13 P)

R

Rank of Matroid Circuit is One Less Than Cardinality‎ (2 P)

Pages in category "Matroid Rank Functions"

The following 18 pages are in this category, out of 18 total.

B

Bounds for Rank of Subset

C

Cardinality of Maximal Independent Subset Equals Rank of Set

E

Equivalence of Definitions of Matroid Rank Axioms

F

Formulation 1 Rank Axioms Implies Rank Function of Matroid

I

Independent Subset is Base if Cardinality Equals Rank of Matroid

M

R

S

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Matroid Theory