Combinatorics: Topics, Techniques, Algorithms

by Peter J. Cameron

• ISBN13: 9780521457613
• ISBN10: 0521457610
• Format: Paperback
• Copyright: 1995-01-27
• Publisher: Cambridge University Press

Summary

Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

Table of Contents

Preface

1. What is combinatorics?

2. On numbers and counting

3. Subsets, partitions, permutations

4. Recurrence relations and generating functions

5. The principle of inclusion and exclusion

6. Latin squares and SDRs

7. Extremal set theory

8. Steiner triple theory

9. Finite geometry

10. Ramsey's theorem

11. Graphs

12. Posets, lattices and matroids

13. More on partitions and permutations

14. Automorphism groups and permutation groups

15. Enumeration under group action

16. Designs

17. Error-correcting codes

18. Graph colourings

19. The infinite

20. Where to from here?

Answers to selected exercises

Bibliography

Index.