Combinatorics Topics, Techniques, Algorithms A textbook in combinatorics for second-year undergraduate to beginning graduate students. Peter J. Cameron (Author) 9780521457613, Cambridge University Press Paperback / softback, published 6 October 1994 368 pages24.7 x 17.4 x 2.4 cm, 0.649 kg "...used as a text at the senior or graduate level and is an excellent reference....The range of topics is very good." The UMAP Journal 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. 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. Subject Areas: Combinatorics & graph theory [PBV]
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