Syllabus MAT 246: Algebraic Combinatorics
Winter 2010

Lectures: MWF 1:00-2:00pm in PHYSIC 140
Office hours: TBA
Instructor: Monica Vazirani, MSB 3224, phone: 554-2596, mjvazirani@ucdavis.edu
Text:
  • Richard P. Stanley, "Enumerative Combinatorics, Volume II" Cambridge Studies in Advanced Mathematics 62, Cambridge University Press 1999.

    • an online version is available here (tba).
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 The only way to really learn and grasp the material is to play and work with it yourself! There will be one or two midterm exams: The problems on the midterm will be (partially) based on the homework problems.
Web: http://www.math.ucdavis.edu/~vazirani/W11/246.html
SmartSite Links for this CRN: MAT 246 001 WQ 2011

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)
See also the official http://www.math.ucdavis.edu/courses/syllabi/grad/mat246.html

Lecture topics

Homeworks

Homework 1 due January 14
Homework 2 due January 28
Homework 3 due February 11
Homework 4 due February 25
Homework 5 due March 11 (?)/ still under construction
Matthew Stamps is took notes in 2009 available here.