Cambridge ; New York : Cambridge University Press, 1994.
viii, 355 p.
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.
(source: Nielsen Book Data)
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. (source: Nielsen Book Data)