Combinatorics, Fall 2025

Class essentials

• Course syllabus
• Course schedule
• Daily topics
• LaTeX tips
• Practice problems (not to be turned in)

Resources and links

• Catalan Addendum, by Richard Stanley.
• Combinatorial Reciprocity Theorems, by Matthias Beck and Raman Sanyal.
• Eulerian Numbers, by T. Kyle Petersen.
• Igor Pak's Catalan numbers page.

Homework

• HW 1: pdf | tex Topics: Pigeonhole principle and induction. Due Tuesday, September 2, 2025.
  
• HW 2: pdf | tex Topics: Binomial theorem, combinatorial reciprocity. Due Wednesday, September 17, 2025.
  
• HW 3: pdf | tex Topics: Lattice paths, generating functions, partitions. Due Wednesday, September 24, 2025.
  
• HW 4: pdf | tex Topics: Generating functions, partitions, and compositions. Due Friday, October 3, 2025.
  
• HW 5: pdf | tex Topics: Permutations. Due Friday, October 10, 2025.
  
• HW 6: pdf | tex Topics: Mahonian and Eulerian statistics. Due Friday, October 24, 2025.
  
• HW 7: pdf | tex Topics: The Catalan numbers. Due Wednesday, November 5, 2025.
  
• HW 8: pdf | tex Topics: Chip firing and the critical group. Due Monday, November 21, 2025.
  
• HW 9: pdf | tex Topics: The Tutte polynomial, Mobius inversion. Due Monday, December 8, 2025.