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Math 501: Combinatorics

This is an introductory graduate-level course on combinatorics. We will be covering the theory of enumeration, generating functions, combinatorial species, the basics of graph theory, posets, partitions and tableaux, and symmetric function theory. This is the first of a two-semester course, and in the second semester (Math 502) we will be covering more advanced topics and applications of the tools we have developed in the first semester.


For more details, see the Course Syllabus.


The textbook series for the course is Enumerative Combinatorics, Vol. I and II, by Richard Stanley. This is a mandatory book, both for the course and for basic survival in mathematics.

We may also be making use of material from the book Combinatorial Species and Tree-like Structures by François Bergeron, Gilbert Labelle, and Pierre Leroux. This book is optional but may come in handy during this course.

For an excellent resource on partition theory and bijections, see Igor Pak’s survey.

For notes on group actions and counting with symmetry, see Alexander Hulpke’s Notes.

Office hours

My office is Weber 112, right across from the mail room. Come find me:


Homework assignments will be posted here as the course progresses.

Homework 1

Homework 2

Homework 3 - Solutions by Lander Ver Hoef

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8 - Solutions by Lander Ver Hoef

Homework 9

Homework 10

Homework 11

Homework 12

Homework 13

Homework 14 (Last Homework!)

Take-home Final Exam

The take-home portion of the final is posted here: Take-Home Final

The Qualifying Exam will be separate from the course grading, and will be held at the final exam time for this class, which is Tuesday, Dec 17, from 4:10 to 6:10 pm in room E104 (the usual classroom).