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Everything about Matroid representation
Vectors with given pattern of independence
In the mathematical theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations are analogous to group representations; both types of representation provide abstract algebraic structures with concrete descriptions in terms of linear algebra. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matroid representationA 5-minute orientation
- Skim a recent paper: The $\alpha$-Representation for Tait Coloring and the Characteristic Polynomial of a MatroidInfluential work since 2022
- Pick up a classic book: Boolean Representations of Simplicial Complexes and MatroidsThe most-reprinted book on the subject
- Read the landmark paper: Matroid representation over GF(3)Cited 70 times
- Go sideways: Algebraic matroidA closely related topic
- Go sideways: MatroidA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Matroid representation over GF(3)
Partial Fields and Matroid Representation
Partial Matroid Representations
Recent work in matroid representation theory
Common information, matroid representation, and secret sharing for matroid ports
Matroid representation of clique complexes
Matroid Representation of Projective Spaces
A two-dimensional topological representation theorem for matroid polytopes of rank 4
🆕 Influential since 2022
📚 Books worth reading
Boolean Representations of Simplicial Complexes and MatroidsJohn Rhodes, Pedro V. Silva · 2015- 📕Representations of matroidsNorman E. Fenton · 1981
- 📕Representations of MatroidsNorman Elliot Fenton · 1981
- 📕Excluding a Line from Complex-Representable MatroidsJames Geelen, Peter Nelson · 2025
- 📕Focus on African diaspora mathematicsToka Diagana · 2008
The Travelling Salesman Problem and Its VariationsGregory Gutin · 2002
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Algebraic matroid In mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence.…
- Matroid In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many…
- Regular matroid In mathematics, a regular matroid is a matroid that can be represented over all fields. A matroid is defined to be a family of subsets of a finite set…
- Pregeometry (model theory) Pregeometry, and in full combinatorial pregeometry, are essentially synonyms for "matroid". They were introduced by Gian-Carlo Rota with the intention…
- Matroid rank In the mathematical theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements…
- Basis of a matroid In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent…
- Paving matroid In the mathematical theory of matroids, a paving matroid is a matroid in which every circuit has size at least as large as the matroid's rank. In a matroid…
- Rota's conjecture Rota's excluded minors conjecture is one of a number of conjectures made by the mathematician Gian-Carlo Rota. Some members of the structural combinatorics…