Combinatorics

Week 1 | Week 2 | Week 3

Tuesday, January 25

Class notes

• Paths on Pascal’s triangle
• Paths on a grid
• Forbidden squares
• Integers not divisible by 2, 3, 5
• Fixed-point free permutations

Wednesday, January 26

Office hours

• A binomial identity

Thursday, January 27

Class notes

• Fixed-point free permutations
• Inclusion-exclusion in algebraic geometry

Suggested reading

• 2007 Aigner - A Course in Enumeration
  • 5.1 Inclusion–Exclusion
• 1983 Pólya, Tarjan, Woods - Notes on Elementary Combinatorics
  • 4. Principle of Inclusion and Exclusion
• 2001 Martin - Counting: The art of enumerative combinatorics
  • Chapter 2. The Principle of Inclusion and Exclusion
• 2003 Lovasz, Pelikan, Vesztergombi - Discrete mathematics
  • 2.3 Inclusion-Exclusion
• 2011 Camina, Lewis - An introduction to enumeration
  • 1.3 The Principle of Inclusion and Exclusion
• 2015 Beeler - How to count
  • 7 Advanced Counting — Inclusion and Exclusion