## Combinatorics |

## an upper-level introductory course in enumeration, graph theory, and design theory |

## by Joy Morris |

This free undergraduate text book provides an introduction to enumeration, graph theory, and design theory. It is aimed
at upper-level undergraduate students and the exercises expect some mathematical sophistication, including a reasonable
ability to construct proofs.
The text is designed to be used in an undergraduate course, but could be suitable for independent study by a student with
some mathematical background and understanding of proofs. It does not assume any background knowledge of combinatorics.

The book is being released online with a Creative Commons license (Attribution-NonCommercial-ShareAlike 2.0).
Although not in final form, it has already been used as a textbook for several semesters by 2 different instructors
at the University of Lethbridge.

Click here for a pdf file of the June 2017 version (approximately 250 pages and 1.2 MB)

The LaTeX source files are available by request. E-mail the author to request these.

2. Basic Counting Techniques

3. Permutations, Combinations, and the Binomial Theorem

4. Bijections and Combinatorial Proofs

5. Counting with Repetitions

6. Induction and Recursion

7. Generating Functions

8. Generating Functions and Recursion

9. Some Important Recursively-Defined Sequences

10. Other Basic Counting Techniques

11. Basics of Graph Theory

12. Moving Through Graphs

13. Euler and Hamilton

14. Graph Colouring

15. Planar Graphs

16. Latin Squares

17. Designs

18. More Designs

19. Designs and Codes

Index

List of Notation

Appendix A: Solutions to Selected Exercises