Math 249—Algebraic Combinatorics
Spring 2012

Time and place: TuTh 11-12:30pm, Room 6 Evans Hall

Course control number: 54535

Professor: Mark Haiman
Office: 855 Evans
Office hours: W 10:30am-12:30pm
Phone: (510) 642-4318

Syllabus: Introduction to combinatorics at the graduate level, with topics from the four general areas below.

  1. Enumeration: ordinary and exponential generating functions; Joyal's theory of species.
  2. Symmetric functions and their connection with representation theory of symmetric groups and general linear groups; tableau combinatorics; q-analogs in the theory of symmetric functions. Possibly some discussion of combinatorics and representation theory related to (q,t)-Catalan numbers and parking function enumeration.
  3. Order: posets, lattices and incidence algebras; order polynomials, zeta polynomials. Possibly some discussion of cd-indices and g-polynomials.
  4. Geometric combinatorics: polytopes, hyperplane arrangements, simplicial complexes; Stanley-Reisner rings and Cohen-Macaulay complexes; f-vectors.

Prerequisites: Algebra background equivalent to 250A.

Required text: Richard P. Stanley, Enumerative Combinatorics, Vols. I & II. Cambridge Univ. Press 1999, 2000.

Recommended additional reading:

Homework and grading: Grading is based entirely on homework; no exams. Officially, homework is due the second Tuesday following the lecture for which it is assigned, or the next class day if that Tuesday is a holiday. Problems for the last two weeks of lectures are due by Friday, May 11, the last day of final exam week. To keep up with the lectures you should try to do the problems on time. However, I don't promise to grade and return homework in a timely fashion, so I don't insist that you turn it in on time.

Here is the running list of homework problems, organized by lecture. For your convenience if you are writing solutions on a computer, you can also download the LaTeX source file. Note: problems from Stanley Vol. I refer to the 1st edition (Wadsworth & Brooks/Cole 1986; Cambridge Univ. Press 1997 hardcover, 1999 paperback), not the new 2nd edition (Cambridge Univ. Press 2012).

Lecture topics

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