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Explore the main themes, entities and connections around Matroid. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Definition
27 related topics
Examples
41 related topics
History
9 related topics
Polynomial invariants
10 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Combinatorics
- Linear independence
- Vector spaces Vector space
- Axiomatically Axiomatic system
- Partially ordered sets Partially ordered set
- Geometric lattice
- Linear algebra
- Graph theory
- Geometry
- Topology
- Combinatorial optimization
- Network theory
- Coding theory
- Crapo Henry Crapo (mathematician)
Definition
- Equivalent Cryptomorphism
- Finite set
- Family Family of sets
- Subsets Subset
- Empty set
- Steinitz exchange lemma
- Independence system
- Abstract simplicial complex
- Maximal independent set
- Graphic matroids Graphic matroid
- If and only if
- Bases in linear algebra Basis (linear algebra)
- Rank function Matroid rank
- Integer
- Submodular function
- Monotonic function
- Closure operator
- Power set
- Mac Lane Saunders Mac Lane
- Steinitz Ernst Steinitz
- Maximal Maximal element
- Cover Covering relation
- Matroid lattice
- Atoms Atom (order theory)
- Sperner family
- Minty George J. Minty
- Singleton set Singleton (mathematics)
Examples
- Free matroid
- Natural number
- Uniform matroid
- Geelen, Gerards & Kapoor (2000) Matroid
- Partition matroids Partition matroid
- Represents Matroid representation
- Fano plane
- Finite geometry
- Finite field
- GF(2)
- Real numbers Real number
- Matrix Matrix (mathematics)
- Field Field (mathematics)
- (0,1) matrix Logical matrix
- Rota's conjecture
- Binary matroids Binary matroid
- Tutte W. T. Tutte
- Seymour Paul Seymour (mathematician)
- Regular matroid
- Vámos matroid
- Multigraph
- Forest Tree (graph theory)
- Simple cycle
- Bicircular matroid
- Pseudoforest
- Gammoid
- Bipartite graph
- Matchings Matching (graph theory)
- Dual matroids Dual matroid
- Signed graphs Signed graph
Basic constructions
- Kuratowski's theorem
- Planar graph
- Dual graph
- Minor Matroid minor
- Minor-minimal Minimal element
- Disjoint union
Additional terms
- Girth Matroid girth
- Paving matroid
- Basis polytope Matroid polytope
- Convex hull
- Indicator vectors Indicator vector
Algorithms
Matroid software
Polynomial invariants
- Characteristic polynomial
- Möbius function Möbius function (combinatorics)
- Chromatic polynomial
- Tutte polynomial
- Arrangement Arrangement of hyperplanes
- Stirling numbers Stirling number
- Complete graph
- Partition lattice Partition of a set
- Hassler Whitney
- Gian-Carlo Rota
Infinite matroids
- Pregeometries Pregeometry (model theory)
- Hilbert Hilbert space
- Banach spaces Banach space
- Model theory
- Mathematical logic
- Algebra
History
- Takeo Nakasawa
- Projective geometry
- Richard Rado
- Transversal theory Transversal (combinatorics)
- Tutte homotopy theorem
- Dominic Welsh
- Dowling geometries Dowling geometry
- Geoff Whittle Geoff Whittle?action=edit&redlink=1
- Geelen Jim Geelen
Researchers
- B. L. van der Waerden Bartel Leendert van der Waerden
- Jack Edmonds
- Eugene Lawler
- László Lovász
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Matroid
Nodes144
Edges143
Triples111
Avg. degree1.99
Density0.013889
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Matroid
Top relations
related to External links · 10
Matroid → Brooklyn, Brooklyn College, City University, EMS Press, Encyclopedia, Kingan, Mathematics, New York, NY, Sandra
related to Matroid software · 9
Matroid → Both, Hlineny's Macek, Kingan's Oid, Macaulay2, Macek, Maple, Oid, SAGE, Two
related to history · 8
Matroid → Because, His, In, It, Kuroda, Nishimura, Takeo Nakasawa, Whitney
related to Uniform matroids · 8
Matroid → Additional, All, An, In, Let, One, The, This
see also · 8
Matroid → Abstraction, Antimatroid, Formulation, Generalization, Group-theoretic, Mathematical, Multiset, Set
is a · 7
Matroid → bicircular matroid of G, matroid in which every proper, matroid that is representable over all possible fields, simplest example of a matroid that is not representable over any field, simplest example of a matroid that is not representable over any field.Matroids from graph theoryA second original source for the theory of matroids is graph theory.Every finite…, size of its smallest circuit or dependent set.An element that forms a single-element circuit of M is called a loop, strict gammoid and vice versa.ExampleThe cycle matroid of a graph is the dual matroid of its bond matroid
related to Minors · 5
Matroid → Equivalently, If, In, Its, The
related to Rank functions · 5
Matroid → If, It, R1, The, This
related to Algorithms · 4
Matroid → Finding, In, Several, This
related to Duality · 4
Matroid → For, If, It, The
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
displaystyle set matroids called rank independent theory sets subset subsets finite every graph elements element field one polynomial linear equivalent
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Matroid | is a | matroid in which every proper | 0.90 | text |
| Matroid | is a | matroid that is representable over all possible fields | 0.90 | text |
| Matroid | is a | simplest example of a matroid that is not representable over any field.Matroids from graph theoryA second original source for the theory of matroids is graph theory.Every finite… | 0.90 | text |
| Matroid | is a | bicircular matroid of G | 0.90 | text |
| Matroid | is a | simplest example of a matroid that is not representable over any field | 0.90 | text |
| Matroid | is a | strict gammoid and vice versa.ExampleThe cycle matroid of a graph is the dual matroid of its bond matroid | 0.90 | text |
| Matroid | is a | size of its smallest circuit or dependent set.An element that forms a single-element circuit of M is called a loop | 0.90 | text |
| Matroid | related to Additional terms | Let | 0.60 | section |
| Matroid | related to Additional terms | Its | 0.60 | section |
| Matroid | related to Algorithms | Several | 0.60 | section |
| Matroid | related to Algorithms | In | 0.60 | section |
| Matroid | related to Algorithms | Finding | 0.60 | section |
No triples extracted yet.
Related concept clusters Concept neighborhoods
Clusters of nearby vocabulary surrounding the topic. Scan them for adjacent concepts and language you may have missed.These clusters group vocabulary that occurs around closely connected concepts in the source material.
Connections between topic areas Semantic bridges
Bridge nodes connect otherwise separate parts of the map. Expand a row to inspect the topic groups on each side.Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.
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