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.

Books

The textbook series for the course is Enumerative Combinatorics, Vol. I and II, by Richard Stanley. A parallel supplemental resource that I also suggest taking a look at is The Art of Counting by Bruce Sagan.

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.