Text by a noted expert describes standard examples and investigation results, using elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. Includes numerous exercises. 1976 edition.
The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. Aimed at advanced undergraduate and graduate students, this text is one of the earliest substantial works on matroid theory. Its author, D. J. A. Welsh, Professor of Mathematics at Oxford University, has exercised a profound influence over the theory's development. The first half of the text describes standard examples and investigation results, using elementary proofs to develop basic matroid properties and referring readers to the literature for more complex proofs. The second half advances to a more sophisticated treatment, addressing a variety of research topics. Praised by the Bulletin of the American Mathematical Society as ""a useful resource for both the novice and the expert,"" this text features numerous helpful exercises.
By:
D J A Welsh
Imprint: Dover
Country of Publication: United States [Currently unable to ship to USA: see Shipping Info]
Dimensions:
Height: 214mm,
Width: 136mm,
Spine: 22mm
Weight: 457g
ISBN: 9780486474397
ISBN 10: 0486474399
Series: Dover Books on Mathema 1.4tics
Pages: 433
Publication Date: 17 June 2010
Audience:
General/trade
,
ELT Advanced
Format: Paperback
Publisher's Status: Unspecified
Preface Preliminaries 1. Fundamental Concepts and Examples 2. Duality 3. Lattice Theory and Matroids 4. Submatroids 5. Matroid Connection 6. Matroids, Graphs and Planarity 7. Transversal Theory 8. Covering and Packing 9. The Vector representation of Matroids 10. Binary Matroids 11. Matroids from Fields and Groups 12. Block Designs and matroids 13. Menger's Theorem and Linkings in Graphs 14. Transversal Matroids and Related Topics 15. Polynomials, Colouring Problems, Codes and packings 16. Extremal Problems 17. Maps between Matroids and Geometric Lattices 18. Convex Polytopes associated with Matroids 19. Combinatorial OPtimisation 20. Infinite Structures Bibliography Index of Symbols Index
