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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 on combinatorics.


For more details, see the Course Syllabus.


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.


Homework assignments will be posted here as the course progresses.

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Homework 9

Homework 10

Homework 11

Homework 12

Homework 13

Homework 14

Optional Homework/Final Exam Review

Class Notes

Lecture 1

Lecture 2

Lecture 3

Lectures 4-5

Lecture 6

Lectures 7-8

Lectures 9-11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lectures 22-23

Lecture 24

Lectures 25-26

Lecture 27

Lecture 28

Lectures 29-30

Lecture 31

Lectures 32-33

Lectures 34-35

Lecture 36

Lecture 37

Lecture 38

Lecture 39

Lecture 40

Lecture 41

Lecture 42