# Category:Matroid Theory

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This category contains results about Matroid Theory.

Definitions specific to this category can be found in Definitions/Matroid Theory.

**Matroid Theory** is the branch of mathematics which concerns the role which matroids play in disparate branches of combinatorial theory and algebra such as graph theory, lattice theory, combinatorial optimisation, and linear algebra.

## Pages in category "Matroid Theory"

The following 37 pages are in this category, out of 37 total.

### L

- Leigh.Samphier/Sandbox/Alternative Axiomatization of Matroid
- Leigh.Samphier/Sandbox/Closure of Subset Contains Parallel Elements
- Leigh.Samphier/Sandbox/Definition:Extended Weight Function
- Leigh.Samphier/Sandbox/Definition:Greedy Algorithm/Maximum Weight Problem
- Leigh.Samphier/Sandbox/Definition:Maximum Weight Problem
- Leigh.Samphier/Sandbox/Distinct Elements are Parallel iff Each is in Closure of Other
- Leigh.Samphier/Sandbox/Distinct Elements are Parallel iff Pair forms Circuit
- Leigh.Samphier/Sandbox/Element is Member of Base iff Not Loop
- Leigh.Samphier/Sandbox/Loop Belongs to Every Flat
- Leigh.Samphier/Sandbox/Matroid Contains No Loops iff Empty Set is Flat
- Leigh.Samphier/Sandbox/Matroid satisfies Base Axiom
- Leigh.Samphier/Sandbox/Matroid satisfies Rank Axioms
- Leigh.Samphier/Sandbox/Parallel Elements Depend on Same Subsets
- Leigh.Samphier/Sandbox/Parallel Relationship is Transitive
- Leigh.Samphier/Sandbox/Set with Two Parallel Elements is Dependent

### M

### S

- Singleton is Dependent implies Rank is Zero
- Singleton is Dependent implies Rank is Zero/Corollary
- Singleton is Independent iff Rank is One
- Singleton is Independent implies Rank is One
- Singleton is Independent implies Rank is One/Corollary
- Superset of Dependent Set is Dependent
- Superset of Dependent Set is Dependent/Corollary