Course Syllabus

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Lectures: MWF 12:10-1pm in OLSON 223

Office hours: You can talk to me after every class! Otherwise drop me an e-mail to set up a time to talk.

Instructor: Anne Schilling, MSB 3222, e-mail: anne@math.ucdavis.edu

Text:

  • Richard Stanley, "Enumerative Combinatorics, Volume II", Cambridge Studies in Advanced Mathematics 62, Cambridge University Press

Other useful texts include:

  • William Fulton, "Young tableaux", London Mathematical Society, Student Texts 35, Cambridge University Text 1997
  • Bruce E. Sagan, "The symmetric group, representations, combinatorial algorithms, and symmetric functions", Springer, second edition, 2001
  • I.G. Macdonald, "Symmetric functions and Hall polynomials", Oxford Science Publication, second edition, 1995

Prerequisites: MAT 245; or permission by instructor

Grading: There will be regularly assigned homeworks, which are due every second Friday in class. Please hand in at least one problem from each homework set. Also, every student should present at least 1-2 problems in class in the course of the entire quarter. Problems are discussed every second Friday. The only way to really learn and graps the material is to play around with it and work with it yourself!

Course Description

Algebraic combinatorics at the graduate level, covering the following topics:

  1. The ring of symmetric functions
  2. Various bases for the ring of symmetric functions
  3. Combinatorial definition of Schur functions
  4. RSK algorithm
  5. Littlewood-Richardson and Pieri rule
  6. Knuth relations
  7. Differential posets
  8. Murnaghan-Nakayama rule
  9. Further topics (time permitting): LLT polynomials, Macdonald polynomials, quasisymmetric functions, k-Schur functions

Course Summary:

Date Details Due