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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.
"Cameron covers an impressive amount of material in a relatively small space...an outstanding supplement to other texts..." M. Henle, Choice
P. J. Cameron, J. H. van Lint, P. J. (Queen Mary University of London) Cameron, The Netherlands) Lint, J. H. van (Technische Universiteit Eindhoven, J. H. Van Lint, Peter J. Cameron
P. J. Cameron, J. H. van Lint, P. J. (Queen Mary University of London) Cameron, The Netherlands) Lint, J. H. van (Technische Universiteit Eindhoven, Peter J. Cameron, J. H. Van Lint
Peter J. Cameron, Pierre-Philippe Dechant, Yang-Hui He, John McKay, Peter J. (University of St Andrews) Cameron, Pierre-Philippe (University of Leeds) Dechant, Yang-Hui (London Institute for Mathematical Sciences) He, Montreal) McKay, John (Concordia University
P. J. Cameron, J. H. van Lint, P. J. (Queen Mary University of London) Cameron, The Netherlands) Lint, J. H. van (Technische Universiteit Eindhoven, J. H. Van Lint, Peter J. Cameron
R. A. Bailey, Peter J. Cameron, Yaokun Wu, Scotland) Bailey, R. A. (University of St Andrews, Scotland) Cameron, Peter J. (University of St Andrews, China) Wu, Yaokun (Shanghai Jiao Tong University
Peter J. Cameron, Pierre-Philippe Dechant, Yang-Hui He, John McKay, Peter J. (University of St Andrews) Cameron, Pierre-Philippe (University of Leeds) Dechant, Yang-Hui (London Institute for Mathematical Sciences) He, Montreal) McKay, John (Concordia University