\space |
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.
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
Vaek Chvátal'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 Erdös Number Project (in collaboration with Patrick Ion and Rodrigo De Castro) |