Theory of Matroids

Buch | Softcover

340 Seiten

2008
Cambridge University Press (Verlag)
978-0-521-09202-9 (ISBN)

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The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

1. Examples and Basic Concepts Henry Crapo; 2. Axiom Systems Giorgio Nicoletti and Neil White; 3. Lattices Ulrich Faigle; 4. Basis-Exchange Properties Joseph P. S. Kung; 5. Orthogonality Henry Crapo; 6. Graphs and Series-Parallel Networks James Oxley; 7. Constructions Thomas Brylawski; 8. Strong Maps Joseph P. S. Kung; 9. Weak Maps Joseph P. S. Kung and Hein Q. Nguyen; 10. Semimodular Functions Hein Q. Nguyen.

Erscheint lt. Verlag	4.12.2008
Reihe/Serie	Encyclopedia of Mathematics and its Applications
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	380 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	0-521-09202-7 / 0521092027
ISBN-13	978-0-521-09202-9 / 9780521092029
Zustand	Neuware