Category:Matroid Theory
Jump to navigation
Jump to search
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 optimization, and linear algebra.
Subcategories
This category has the following 7 subcategories, out of 7 total.
E
M
Pages in category "Matroid Theory"
The following 78 pages are in this category, out of 78 total.
C
D
E
- Element Depends on Independent Set iff Union with Singleton is Dependent
- Element is Loop iff Member of Closure of Empty Set
- Element is Loop iff Singleton is Circuit
- Element is Member of Base iff Not Loop
- Element of Matroid Base and Circuit has a Substitute
- Element of Matroid Base and Circuit has a Substitute/Lemma 1
- Element of Matroid Base and Circuit has a Substitute/Lemma 2
- Element of Matroid Base and Circuit has a Substitute/Lemma 3
- Equivalence of Definitions of Matroid
- Equivalent Conditions for Element is Loop
I
- Independent Set can be Augmented by Larger Independent Set
- Independent Set can be Augmented by Larger Independent Set/Corollary
- Independent Subset is Base if Cardinality Equals Cardinality of Base
- Independent Subset is Base if Cardinality Equals Rank of Matroid
- Independent Subset is Base if Cardinality Equals Rank of Matroid/Corollary
- Independent Subset is Contained in Base
- Independent Subset is Contained in Maximal Independent Subset
- Independent Subset of Matroid is Augmented by Base
L
- Leigh.Samphier/Sandbox/Bound for Cardinality of Matroid Circuit
- Leigh.Samphier/Sandbox/Cardinality of Maximal Independent Subset Equals Rank of Set
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Base Axiom
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Circuit Axioms
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms/Condition 1 Implies Condition 3
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms/Condition 1 Implies Condition 3/Lemma 1
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms/Condition 1 Implies Condition 3/Lemma 2
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms/Condition 1 Implies Condition 3/Lemma 3
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms/Condition 2 Implies Condition 1
- Leigh.Samphier/Sandbox/Equivalence of Definitions of Matroid Rank Axioms/Condition 3 Implies Condition 2
- Leigh.Samphier/Sandbox/Independent Subset is Contained in Maximal Independent Subset/Corollary
- Leigh.Samphier/Sandbox/Independent Superset of Dependent Set Minus Singleton Doesn't Contain Singleton
- Leigh.Samphier/Sandbox/Matroid Base Axiom Implies Sets Have Same Cardinality
- Leigh.Samphier/Sandbox/Matroid Base Substitution From Fundamental Circuit
- Leigh.Samphier/Sandbox/Matroid Satisfies Base Axiom
- Leigh.Samphier/Sandbox/Matroid Satisfies Circuit Axioms
- Leigh.Samphier/Sandbox/Matroid satisfies Rank Axioms
- Leigh.Samphier/Sandbox/Matroid satisfies Rank Axioms/Necessary Condition
- Leigh.Samphier/Sandbox/Matroid with No Circuits Has Single Base
- Leigh.Samphier/Sandbox/Proper Subset of Matroid Circuit is Independent
- Leigh.Samphier/Sandbox/Rank of Matroid Circuit is One Less Than Cardinality
- Leigh.Samphier/Sandbox/Set Difference of Matroid Circuit with Element is Independent
- Loop Belongs to Every Flat
M
- Matroid Base Union External Element has Fundamental Circuit
- Matroid Contains No Loops iff Empty Set is Flat
- Matroid Induced by Affine Independence is Matroid
- Matroid Induced by Algebraic Independence is Matroid
- Matroid Induced by Linear Independence in Abelian Group is Matroid
- Matroid Induced by Linear Independence in Vector Space is Matroid
- Matroid Unique Circuit Property
- Matroid Unique Circuit Property/Corollary
R
S
- 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
