Combinatorial Mathematics

This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.

Douglas B. West (Author)

9781107058583, Cambridge University Press

Hardback, published 16 July 2020

988 pages, 2200 exercises
25.2 x 19.8 x 5.7 cm, 2 kg

'This book is impressive both for its breadth and its hundreds of exercises. Serious study of it will richly reward the reader.' Daniel Cranston, Virginia Commonwealth University

This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science. Optional more advanced material also makes it valuable as a research reference. Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material. It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty. Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language. The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.

Introduction
Part I. Enumeration: 1. Combinatorial arguments
2. Recurrence relations
3. Generating functions
4. Further topics
Part II. Graphs: 5. First concepts for graphs
6. Matchings
7. Connectivity and cycles
8. Coloring
9. Planar graphs
Part III. Sets: 10. Ramsey theory
11. Extremal problems
12. Partially ordered sets
13. Combinatorial designs
Part IV. Methods: 14. The probabilistic method
15. Linear algebra
16. Geometry and topology
Appendix. Hints to selected exercises
References
Author index
Notation index
Subject index.

Subject Areas: Combinatorics & graph theory [PBV], Discrete mathematics [PBD]