White N. (ed.) Matroid applications

Cambridge: Cambridge University Press, 2009. - 376 p.This volume, the third in a sequence that began with The Theory of Matroids (1986) and Combinatorial Geometries (1987), concentrates on the applications of matroid theory to a variety of topics from geometry (rigidity and lattices), combinatorics (graphs, codes, and designs) and operations research (the greedy algorithm).Bar Frameworks on the Line - The Graphic Matroid
Bar Frameworks in the Plane
Plane Stresses and Projected Polyhedra
Bar Frameworks in -space
A Matroid from Splines
Scene Analysis of Polyhedral Pictures
Special PositionsHistorical Notes
ExercisesSome Lattice Properties and Parameters of PMDs
Intersection Properties of the Hyperplane Family
PMDs of Rank
Triffids
Some Close Relatives of PMDs and Further DirectionsPre-independence Spaces and Independence Spaces
B-matroids
ExercisesMatroidal Families of Graphs: a Definition
Countably Many Matroidal Families
Uncountably Many Matroidal Families
Digraphs and Infinite Graphs
ExercisesThe Lattice of All Partitions
Lattice Embeddings
Postscript
ExercisesThe Tutte Polynomial
T-G Invariants in Graphs
The Critical Problem
Linear Codes
Other Tutte Invariants
ExercisesShellable Complexes
Matroid Complexes
Broken Circuit Complexes
Application to Matroid Inequalities
Order Complexes of Geometric Lattices
Homology of Shellable Complexes
Homology of Matroids
Homology of Geometric Lattices
The Orlik-Solomon Algebra
Notes and Comments
ExercisesDefinitions and Basic Facts
Examples
Structural Properties
Optimization on Greenoids
The Greedoid Polynomial
Antimatroids
Poset of Flats
Further Topics
Notes and Comments
Exercises