CO 330 -- Combinatorial enumeration, Fall 2026

Information

We will explore combinatorial classes by

• Meeting classical discrete objects
• Counting them
• Finding bijections between classes
• Generating random elements

Instructor: Rowan Yeats (I usually go by Ren). Pronouns he/him or they/them.
Office: MC 5126
Email: ren.yeats at uwaterloo.ca
Office Hours:
Lectures: Mondays, Wednesdays, and Fridays 9:30-10:20, MC 4060
TAs: Zeus Dantas e Moura and Matteus Froese
Syllabus.

References:

• Combinatorial Enumeration course notes by David Wagner
• An Invitation to Enumeration by Stephen Melczer

Office hours:

• Instructor office hours: Mondays 12:30-1:30 and Fridays 11-noon in MC 5126 or by appointment
• TA office hours:
  • Thursdays 4-5 in MC 6311 All weeks, Zeus Dantas e Moura
  • Thursdays 10-11 in MC 5481 Only weeks with an assignment due, Matteus Froese

Announcements

• Wednesday September 9 will be an optional review session of the things that you should remember from MATH 239/249 in order to thrive in this course. The course proper will begin on Friday September 11, when everyone should attend.
• Clarified that in a1 you do not need to use the generalized binomial theorem for question 4 (rather the application of this fact would use the generalized binomial theorem, but you don't need to do that for the assignment question.)
• Information about midterm 1.
• Read this before class Friday Oct 9.
• Midterm 1 solutions.
• Instructions for the video assignment due on Dec 7.
• Matteus Frose' office hours on Thursday October 29 will be virtual, but at the same time as usual. You have been emailed a teams link, ask if you didn't get it but want to attend.

Assignments

Assignments will be less than weekly and due by crowdmark typically on Fridays at 3pm.

1. Assignment 1 due Friday September 25 at 3pm. Solutions.
2. Assignment 2 due Friday October 2 at 3pm. Solutions.
3. Assignment 3 due Friday October 30 at 3pm.
4. Assignment 4 due Friday November 6 at 3pm.
5. Assignment 5 due Friday November 13 at 3pm.

Class Summaries

These summaries are not meant to replace your own notes, but give an overview and useful references. They are summaries not full notes.

Part 0: Introduction and review

1. Lecture 1 summary part 1

Part 1: Combinatorial classes, generating series and combinatorial constructions, Lagrange inversion, and lets sneak in some bijections too.

1. Lecture 1 summary part 2
2. Lecture 2 summary
3. Lecture 3 summary
4. Lecture 4 summary
5. Lecture 5 summary
6. Lecture 6 summary
7. Lecture 7 summary
8. Lecture 8 summary
9. Lecture 9 summary
10. Lecture 10 summary
11. Lecture 11 summary

Part 2: q-counting

1. Lecture 12 summary
2. Lecture 13 summary
3. Lecture 14 summary
4. Lecture 15 summary part 1

Part 3: Integer partitions

1. Lecture 15 summary part 2
2. Lecture 16 summary
3. Lecture 17 summary
4. Lecture 18 summary
5. Lecture 19 summary