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.
This category has only the following subcategory.
- ► Examples of Matroids (12 P)
Pages in category "Matroid Theory"
The following 37 pages are in this category, out of 37 total.
- 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
- 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