Syllabus MAT 246: Algebraic Combinatorics
Winter 2009

Lectures: MWF 1:00-2:00pm in MSB 3106
Office hours: MW 2-3pm
Instructor: Anne Schilling, MSB 3222, phone: 754-9371, anne@math.ucdavis.edu
Text:
  • 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 will not be collected but which you are expected to work on. The only way to really learn and grasp the material is to play and work with it yourself! There will be two midterm exams: an in-class midterm on Friday February 6 and a take-home exam due Monday March 16 in class (contributing 50% each to the final grade). The problems on the midterm will be (partially) based on the homework problems.
Web: http://www.math.ucdavis.edu/~anne/WQ2009/246.html

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

Homeworks

Homework 1 posted January 12
Homework 2 posted January 26
Homework 3 posted February 9
Homework 4 posted February 23
Homework 5 posted March 2
Take-home midterm to be handed in in class Monday March 16: HW3 #5, HW4 #3, HW5 #2 and one problem of your choice (which has not appeared on the midterm)
Matthew Stamps is taking notes available here.