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 on combinatorics.

Syllabus

For more details, see the Course Syllabus.

Resources

What is combinatorics? Here is a list of quotes compiled by Igor Pak.

The textbook for the course is The Art of Counting by Bruce Sagan. We will also make use of material from Enumerative Combinatorics, Vol. I and II, by Richard Stanley. See the Canvas course for links and files.

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.