Course Introduction

• Prerequisite：
• Recommended for： Master
• Introduction：

This is a required course of the Combinatorics Graduate Program. The syllabus of the course will contain half of the topics from the Ph.-D. qualification exam of combinatorics (the other half will be taught in the course "Graph Theory"). Moreover, if time permits, selected topics from Analytic Combinatorics, Enumerative Combinatorics, Combinatorial Design Theory, Design and Analysis of Algorithms, Algebraic Combinatorics, etc. will be presented as well.

• Syllabus：

1. (Ch 6) Dilworth's theorem and extremal set theory
2. (Ch 10) The principle of inclusion and exclusion; inversion formula
3. (Ch 13) Elementary counting; Stirling numbers
4. (Ch 14) Recursions and generating functions
5. (Ch 17) Latin squares
6. (Ch 18) Hadamard matrices, Reed-Muller codes
7. (Ch 19) Designs
8. (Ch 25) Lattices and Mobius inversion

• Reference：

1. A Course in Combinatorics by J. H. van Lint and R. M. Wilson