## Table of contents for Combinatorics : a guided tour / David R. Mazur.

Bibliographic record and links to related information available from the Library of Congress catalog

Information from electronic data provided by the publisher. May be incomplete or contain other coding. Preface; Before you go; Notation; Part I. Principles of Combinatorics: 1. Typical counting questions, the product principle; 2. Counting, overcounting, the sum principle; 3. Functions and the bijection principle; 4. Relations and the equivalence principle; 5. Existence and the pigeonhole principle; Part II. Distributions and Combinatorial Proofs: 6. Counting functions; 7. Counting subsets and multisets; 8. Counting set partitions; 9. Counting integer partitions; Part III. Algebraic Tools: 10. Inclusion-exclusion; 11. Mathematical induction; 12. Using generating functions, part I; 13. Using generating functions, part II; 14. techniques for solving recurrence relations; 15. Solving linear recurrence relations; Part IV. Famous Number Families: 16. Binomial and multinomial coefficients; 17. Fibonacci and Lucas numbers; 18. Stirling numbers; 19. Integer partition numbers; Part V. Counting Under Equivalence: 20. Two examples; 21. Permutation groups; 22. Orbits and fixed point sets; 23. Using the CFB theorem; 24. Proving the CFB theorem; 25. The cycle index and Pólya's theorem; Part VI. Combinatorics on Graphs: 26. Basic graph theory; 27. Counting trees; 28. Colouring and the chromatic polynomial; 29. Ramsey theory; Part VII. Designs and Codes: 30. Construction methods for designs; 31. The incidence matrix, symmetric designs; 32. Fisher's inequality, Steiner systems; 33. Perfect binary codes; 34. Codes from designs, designs from codes; Part VIII. Partially Ordered Sets: 35. Poset examples and vocabulary; 36. Isomorphism and Sperner's theorem; 37. Dilworth's theorem; 38. Dimension; 39. Möbius inversion, part I; 40. Möbius inversion, part II; Bibliography; Hints and answers to selected exercises.

Library of Congress subject headings for this publication:
Combinatorial analysis.