Syllabus MAT 246: Algebraic Combinatorics
Winter 2005

Lectures: TR 1:40-3:00pm in Wellman 101
Office hours: Tuesday 3-4pm, Friday 2-3pm
Instructor: Anne Schilling, Kerr Hall 578, 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: Homework 50%; Quarter Project 50%
Homework assignment (most likely due on February 22): It is expected that every student works independently on the graded homework assignment. The solutions should reflect the students own work and understanding of the material. There will also be problems posed throughout the quarter which will not be graded. Students are encouraged to work on these problems together.
Quarter Project: Every student should work on a project throughout the quarter. It is strongly encouraged that students form groups of size 2-3 to work together on the project. Possible topics will be discussed during the first couple of weeks of class. Students are expected to present their projects in form of a talk at the end of the quarter. Click here for a list of suggested topics.
Web: http://www.math.ucdavis.edu/~anne/WQ2005/246.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) polytopes (time permitting)

Lecture topics