Matroid Applications

Matroid Applications

by Neil White
     
 

ISBN-10: 0521119677

ISBN-13: 9780521119672

Pub. Date: 09/17/2009

Publisher: Cambridge University Press

This volume, the third in a sequence that began with Theory of Matroids and Combinatorial Geometries, 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). As with its predecessors, the contributors to this volume have…  See more details below

Overview

This volume, the third in a sequence that began with Theory of Matroids and Combinatorial Geometries, 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). As with its predecessors, the contributors to this volume have written their articles to form a cohesive account so that the result is a volume that will be a valuable reference for research workers.

Product Details

ISBN-13:
9780521119672
Publisher:
Cambridge University Press
Publication date:
09/17/2009
Series:
Encyclopedia of Mathematics and its Applications Series, #40
Pages:
376
Product dimensions:
6.14(w) x 9.21(h) x 0.79(d)

Table of Contents

List of Contributors
Preface
1Matroids and Rigid Structures1
1.1Bar Frameworks on the Line--The Graphic Matroid1
1.2Bar Frameworks in the Plane3
1.3Plane Stresses and Projected Polyhedra11
1.4Bar Frameworks in 3-space16
1.5A Matroid from Splines24
1.6Scene Analysis of Polyhedral Pictures29
1.7Special Positions36
1.8Conclusions39
1.9Historical Notes40
Exercises41
References51
2Perfect Matroid Designs54
2.1Introduction54
2.2Some Lattice Properties and Parameters of PMDs56
2.3Intersection Properties of the Hyperplane Family58
2.4PMDs of Rank 462
2.5Triffids64
2.6Some Close Relatives of PMDs and Further Directions68
References71
3Infinite Matroids73
3.1Pre-independence Spaces and Independence Spaces73
3.2B-matroids80
Exercises86
References89
4Matroidal Families of Graphs91
4.1Introduction91
4.2Matroidal Families of Graphs: a Definition92
4.3Countably Many Matroidal Families96
4.4Uncountably Many Matroidal Families98
4.5Digraphs and Infinite Graphs101
Exercises102
References104
5Algebraic Aspects of Partition Lattices106
5.1Introduction106
5.2The Lattice of All Partitions107
5.3Lattice Embeddings112
5.4Postscript118
Exercises119
References120
6The Tutte Polynomial and Its Applications123
6.1Introduction123
6.2The Tutte Polynomial124
6.3T-G Invariants in Graphs136
6.4The Critical Problem162
6.5Linear Codes181
6.6Other Tutte Invariants188
Exercises197
References215
7Homology and Shellability of Matroids and Geometric Lattices226
7.1Introduction226
7.2Shellable Complexes228
7.3Matroid Complexes232
7.4Broken Circuit Complexes238
7.5Application to Matroid Inequalities242
7.6Order Complexes of Geometric Lattices248
7.7Homology of Shellable Complexes252
7.8Homology of Matroids255
7.9Homology of Geometric Lattices259
7.10The Orlik-Solomon Algebra264
7.11Notes and Comments267
Exercises270
References281
8Introduction to Greedoids284
8.1Introduction284
8.2Definitions and Basic Facts286
8.3Examples293
8.4Structural Properties302
8.5Optimization on Greenoids308
8.6The Greedoid Polynomial313
8.7Antimatroids319
8.8Poset of Flats327
8.9Further Topics335
8.10Notes and Comments343
Exercises348
References354
Index358

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >