CO 430/630 -- Algebraic enumeration, Winter 2026

Information

This course is about algebraic tools for enumeration, as the title suggests, so a big part of that is generating series, now finally with more rigour and with various variants in all their glory. Other important topics include posets and möbius inversion; sign reversing involutions; transfer matrices. There are some classic examples that we'll do as we go along that you as a combinatorialist should know. We will also talk a little about combinatorial species, though this isn't primarily a species course the way I will teach it. In the reverse direction, I will probably tuck some Hopf algebras in, which you should not expect from another instructor.

Instructor: Ren Yeats (either Karen or Ren is fine at this point). Pronouns they/them or he/him. Generally, please, masculine terms when ungendered ones are not readily available.
Office:MC 5126
Email: kayeats at uwaterloo.ca
Office Hours: Mondays 3-5 in MC 5126 or by appointment
Lectures: Mondays and Wednesdays 10:00-11:30, MC 5417
TA: Jerónimo Valencia, TA office hours Tuesdays 2-3 in MC 5472
Syllabus.

Announcements

• On the first day we will vote on details of the course, like what the exams will look like, when my office hours will be, and do we want an online discussion forum, so please come and contribute your view and your vote.
• We agreed on an oral midterm and a written final. My office hours will be Mondays 3-5 starting January 12.
• Jerónimo's office hours will be Tuesdays 2-3 in MC 5472 starting January 13.
• On account of the snow day, my office hours on Jan 26 will be via zoom. Check your email or the discord for the link.
• My office hours on Monday Feb 2 are cancelled. Email or message me if you'd like to arrange to talk another time.
• Midterm instructions and questions to prepare, and rubric.
• The final exam will be a closed book, written exam in the registrar-scheduled slot which is Thursday April 16 from 7:30pm to 10pm in MC 4064.
• Typo in a2 corrected. And another one; if you grade me on this assignment I don't think I'm going to get a very good grade.
• My office hours on Monday Mar 2 will end 15 minutes early at 4:45pm. Email or message me if you'd like to arrange to talk outside of office hours.
• Project guidelines. Key points, 10-15 min presentation in class some time in the last three weeks. Written (or other) part due April 6 at 4pm.
• Jerónimo's office hours cancelled Tuesday March 17.
• a3 did not manage to be typo-free either, and is now corrected. And another one again!
• As we move into the exam period, I will continue to have my regular Monday 3pm-5pm office hours on Monday April 6 and on Monday April 13. I will also have extra office hours Wednesday April 15 from 1:30pm-3:00pm.
• Information about the final exam.

Assignments

Assignments will be less than biweekly and due by crowdmark typically on Wednesdays at 10am.

1. Assignment 1 due Wednesday January 28 at 10am. Solutions.
2. Assignment 2 due Friday March 6 at 10am. Solutions.
3. Assignment 3 due Wednesday April 1 at 10am. Solutions.

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

1. Lecture 1 summary part 1.

Part 1: Formal power series and ordinary generating series

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 part 1.

Part 2: Labelled counting, exponential generating series, and combinatorial species

1. Lecture 8 summary part 2.
2. Lecture 9 summary.
3. Lecture 10 summary.
4. Lecture 11 summary.
5. Lecture 12 summary.

Part 3: Posets, Möbius inversion, and Hopf algebras

1. Lecture 13 summary.
2. Lecture 14 summary.
3. Lecture 15 summary.
4. Lecture 16 summary.
5. Lecture 17 summary.
6. Lecture 18 summary.
7. Lecture 19 summary.