MATH 246: Algebraic Combinatorics
Winter 2015, UC Davis

Lectures: MWF 1:10-2:00pm in Hart Hall 1120
Office hours: M 4-5pm
Instructor: Anne Schilling, MSB 3222, phone: 554-2326,
  • Richard P. Stanley, "Enumerative Combinatorics, Volume II" Cambridge Studies in Advanced Mathematics 62, Cambridge University Press 1999.
Other very useful texts:
  • 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 grasp the material is to play and work with it yourself!

Course description

Algebraic combinatorics at the graduate level, covering the following main topics:
(1) The ring of symmetric functions
(2) Various bases of symmetric functions
(3) Combinatorial definition of the Schur function
(4) RSK algorithm
(5) Littlewood-Richardson rule
(6) Characters of the symmetric group
(7) Further topics (time permitting)

Lecture topics


Homework 1 due Friday January 16, 2015 (Problems 4, 7, 8 will appear again on HW 2 since we won't have covered scalar products by Friday 1/16.)
Homework 2 due Friday January 30, 2015
Homework 3 due Friday February 13, 2015
Homework 4 due Friday February 27, 2015
Homework 5 due Friday March 13, 2015