18.212 Spring 2020
Algebraic Combinatorics

Lectures: Monday and Wednesday 9:30-11, room 4-153

Instructor: Thomas Lam, room 2-169, tfylam@mit.edu

Office hours: Monday and Wednesday, 1-2pm

Course description: We will discuss applications of algebra to combinatorics and vice versa. Topics may include: graph eigenvalues, random walks, domino tilings, matrix tree theorem, electrical networks, Eulerian tours, permutations, partitions, Young diagrams, Young tableaux, Sperner's theorem, Gaussian coefficients, RSK correspondence, partially ordered sets, ...
Level: advanced undergraduate

Grading: Based on several problem sets. There will be no exams.

Going online: Beginning March 12,


Problem sets: There will be problem sets every two weeks. Homework solutions must be typed in LaTeX and either submitted at the beginning of class, or emailed to me before midnight (i.e. by 11:59pm) of the due date. Late homework grades are penalized 20% per late day.
At the front of your homework solution, please acknowledge any books, online sources, etc. consulted, and indicate other students you worked with on the homework.

Problem Set 1 (Due Wednesday February 19) Solutions
Problem Set 2 (Due Wednesday March 4) Solutions
Problem Set 3 (Now Due Wednesday April 1) Solutions
Problem Set 4 (Due Wednesday April 15) Solutions
Problem Set 5 (Due Thursday April 30) Solutions
Problem Set 6 (Due Monday May 11)
Email your psets to kbeuchot@mit.edu and tfylam@mit.edu

The course will have significant overlap with the following optional textbook:
[AC]  Algebraic Combinatorics: Walks, Trees, Tableaux, and More by R. P. Stanley, Springer, 2nd ed, 2018. Version of 2013 is available as pdf file

Additional reading:

[EC1]   [EC2]  Enumerative Combinatorics, Vol 1 and Vol 2, by R. P. Stanley, Cambridge University Press, 2011 and 2001. Volume 1 is available as pdf file

[vL-W]  A Course in Combinatorics by J. H. van Lint and R. M. Wilson, Cambridge University Press, 2001.

List of lectures: