Combinatorics

Course taught in English at the Math in Moscow programme for international undergraduate students at the Independent University of Moscow, Spring 2011.

Problems

1. Basic Enumeration
2. Power Series and Generating Functions
3. Lagrange Inversion and Catalan Numbers
4. Nonintersecting Paths
5. Generating Functions and Asymptotics
6. Midterm | Solutions
7. Partitions
8. Partitions II
9. Dirichlet Generating Functions
10. Arithmetic Functions
11. Trees
12. Exponential Formula
13. Graphs on Surfaces
14. Various Problems on Graphs
15. Extra Problems
16. Final | Solutions

Textbooks

• S. Lando, Lectures on generating functions.
• R. Stanley, Enumerative combinatorics.
• I. P. Goulden and D. M. Jackson, Enumerative combinatorics.
• R. Graham, D. Knuth, O. Patashnik, Concrete mathematics.