Peter J. CameronCambridge University Press, 10/6/1994EAN 9780521457613, ISBN10: 0521457610Paperback, 368 pages, 23.5 x 19 x 2.1 cmLanguage: EnglishCombinatorics 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.Preface1. What is combinatorics?2. On numbers and counting3. Subsets, partitions, permutations4. Recurrence relations and generating functions5. The principle of inclusion and exclusion6. Latin squares and SDRs7. Extremal set theory8. Steiner triple theory9. Finite geometry10. Ramsey's theorem11. Graphs12. Posets, lattices and matroids13. More on partitions and permutations14. Automorphism groups and permutation groups15. Enumeration under group action16. Designs17. Error-correcting codes18. Graph colourings19. The infinite20. Where to from here?Answers to selected exercisesBibliographyIndex.
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