(8/21) Welcome to Math 249! Watch this page for further information.
Mark Haiman,
Office hours Mondays 12:00-1:30 or by appointment
MWF 3-4 pm, 289 Cory
Following this approach, we will still naturally encounter many ideas and objects of interest in classical combinatorial enumeration, such as ordinary and exponential generating functions, symmetric functions, partitions, trees, lattice paths and so on. Our aim will be to connect these things with symmetric groups, considered as Coxeter groups, and with other data associated with root systems of 'type A,' so as to inquire about deeper phenomena and generalize to other root systems.
Although we will pass more quickly over certain topics which I traditionally cover in detail (such as species), in their place we should be able to introduce Hecke algebras and Kazhdan-Lusztig polynomials, and touch on some topics of current research interest, such as k-Schur functions, LLT pollynomials, and q,t-analogs of combinatorics associated with Dyck paths.
The UC library links above should work from computers on campus. You can access library resources from off campus by using 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 may turn in problems in class, at my office (slip them under the door if I'm not in), or by e-mail in PDF format.