(3/17) Updated Problem Set 1 again to fix another mistake in
(3/11) Problem Set 1 has been updated to fix the missing portion of problem 13.
(3/10) While in-person classes are suspended at Berkeley because of corona virus, I'll hold class on Zoom. I've sent out the link to join the Zoom meeting by email. If you didn't receive it, please let me know.
(2/28) Problem Set 1 posted; due March 18 (last class before Spring Break).
(1/21) Welcome to Math 249! Watch this page for further information.
Office hours by appointment
MW 2-3:30, 736 Evans
Next we will turn to the combinatorial theory associated with symmetric functions and representations of the symmetric and general linear groups, including Young tableaux, jeu-de-taquin, and the Frobenius characteristic map. We will see how to re-interpret the cycle index of a combinatorial species using these ideas.
Finally, we will consider "q-analogs" and even "q,t-analogs" of combinatorial concepts encountered in the first part of the course. These may include some or all of: Hall-Littlewood and Macdonald polynomials, Hecke algebras and LLT polynomials, k-Schur functions, and q,t-analogs of combinatorics associated with Catalan numbers.
Depending on how much time we have, we may also discuss how some of the combinatorics associated with the symmetric and general linear groups—which are the Coxeter groups and Lie groups associated with root systems of type A—extends to other root systems.
The online links above are available through the UC Libraries and should work from computers on campus. To access library resources from off campus, you can use the library Proxy Server.
I'll post problem sets below at irregular intervals, generally due 2-3 weeks after posting. Grades will be based on homework. There will be no exams. To get an A in the course, you should do most of the problems, not skipping the harder ones. For a B (or less), some smaller fraction of the assigned work will suffice.
You will need to submit problem sets by e-mail in PDF format, since in-person classes have been cancelled and access to the campus is curtailed because of the Covid-19 pandemic.