Matroid Theory (original) (raw)
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by Sandra Kingan (skingan@brooklyn.cuny.edu).
Matroids are an abstraction of several combinatorial objects, among them graphs and matrices. The word matroid was coined by Whitney in 1935 in his landmark paper "On the abstract properties of linear dependence". In defining a matroid Whitney tried to capture the fundamental properties of dependence that are common to graphs and matrices. Almost simultaneously, Birkhoff showed that a matroid can be interpreted as a geometric lattice. Maclane showed that matroids have a geometric representation in terms of points, lines, planes, dimension 3 spaces etc. Often the term combinatorial geometry is used instead of simple matroids. However, combinatorial geometry has another meaning in mathematical literature. Rank 3 combinatorial geometries are frequently called linear spaces. Matroids are a unifying concept in which some problems in graph theory, design theory, coding theory, and combinatorial optimization become simpler to understand.
Books. This page has a chronological list of matroid books including collections of papers, applications and generalizations. A good textbook on matroids is James Oxley's book Matroid Theory. Click here for a Postscript file containing an errata and update on conjectures, problems, and references.
Surveys. This page has a chronological list of survey papers related to matroids. Many of them serve as entry points into particular matroid topics or matroid generalizations. These papers also have lengthy bibliographies and many open problems. There are links to copies of some papers which serve as a quick overview of the subject.
A Toast to Matroids by W. T. Tutte .
Home Pages of people in Matroid Theory . This page has list of mathematicians working in matroid theory with links to their home pages.
Oid - a software system for experimenting with matroids. This page has information on Oid and links to other matroid and combinatorial software.
Matroid Bibliography: A - D, E - H, I - L, M - P, Q - T, U - Z.
Many thanks to James Oxley for generously allowing me to post on the web all the references in his book.
Matroid Links
The academic family tree of John Hammersley
The Contributions of Dominic Welsh to Matroid Theory by James Oxley.
Alexandre Borovik's Coxeter Matroids
Lukas Finschi's Oriented Matroids Site
Steve Pagano's Matroids and Signed Graphs
Thomas Zaslavsky's Matroid Miscellany and survey of signed and gain graphs
G�nter Ziegler's survey of Oriented Matroids
Combinatorics Links
Va�ek Chv�tal's perfect papers
Peter Cameron's design resources and permutation groups resources
Bill Chen's Combinatorics.net and Hyperbook of combinatorics
The combinatorial object server
Joseph Culberson's Graph Coloring Page
Joe Fields' On-line Dictionary of Combinatorics
Stephen Locke's Graph Theory and Graph Theory Books
Brendan McKay's collection of combinatorial data
MegaMath at Los Alamos
John Noonan's Hyperbook of Combinatorics
Neil Robertson's Algorithmic Problems on Graph Minors
Gordon Royle's Combinatorial Catalogues
Daniel Sander's Graph Theory Resources
Neil Sloane's On-Line Encyclopedia of Integer Sequences
Neil Sloane and Gabriele Nebe's Catalogue of Lattices
Douglas Stinson and Ruizhong Wei's Bibliography on Secret Sharing Schemes and Bibliography on Authentication Codes
Robin Thomas' page on The Four Color Theorem
The Electronic Journal of Combinatorics which maintains a list of Home pages of combinatorial people and groups
Jerry Grossman's Erd�s Number Project (in collaboration with Patrick Ion and Rodrigo De Castro)
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