Book:Dominic Welsh/Matroid Theory

Subject Matter

 * Matroid Theory

Contents

 * Preface


 * Preliminaries 
 * 1 $\quad$ Basic notation
 * 2 $\quad$ Set theory notation
 * 3 $\quad$ Algebraic structures
 * 4 $\quad$ Graph theory


 * Chapter 1. Fundamental Concepts and Examples
 * 1 $\quad$ Introduction
 * 2 $\quad$ Axiom systems for a matroid
 * 3 $\quad$ Examples of matroids
 * 4 $\quad$ Loops and parallel elements
 * 5 $\quad$ Properties of independent sets and bases
 * 6 $\quad$ Properties of the rank function
 * 7 $\quad$ The closure operator
 * 8 $\quad$ Closed sets = flats = subspaces
 * 9 $\quad$ Circuits
 * 10$\quad$ The cycle matroid of a graph
 * 11$\quad$ A Euclidean representation of matroids of rank $\le 3$


 * Chapter 2. Duality
 * 1 $\quad$ The dual matroid
 * 2 $\quad$ The hyperplanes of a matroid
 * 3 $\quad$ Paving matroids
 * 4 $\quad$ The cocycle matroid of a graph


 * Chapter 3. Lattice Theory and Matroids
 * 1 $\quad$ Brief review of lattice theory
 * 2 $\quad$ The lattice of flats of a matroid
 * 3 $\quad$ Geometric lattices and simple matroids
 * 4 $\quad$ Partition lattices and Dilworth’s embedding theorem


 * Bibliography


 * Index of symbols


 * Index