MATH 246: Algebraic Combinatorics
Winter 2017, UC Davis

Lectures: MWF 5:10-6:00pm in Veihmeyer 116
Office hours: You can talk to me after every class! Otherwise drop me an e-mail to set up a time.
Instructor: Anne Schilling, MSB 3222, phone: 554-2326, 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 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!
Web: http://www.math.ucdavis.edu/~anne/WQ2017/246.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

Sage Code on Symmetric Functions

Symmetric functions and asymptotics of number of partitions
Number of partitions with an even number of even parts
Tableaux and RSK in Sage

Homeworks

Homework 1 due Friday January 20, 2017
Homework 2 due Friday February 3, 2017
Homework 3 due Friday February 17, 2017
Homework 4 due Friday March 3, 2017
Homework 5 due Friday March 17, 2017