Topic for Winter 2005: Symmetric functions.
Course meets: TuTh 11:40-1:00, Room 3096 East Hall.
Instructor: Sergey Fomin, 2858 East Hall, 764-6297, fomin@umich.edu
Course homepage: http://www.math.lsa.umich.edu/~fomin/664w05.html
Level: introductory graduate.
Prerequisites: none (for graduate students).
Student work expected: several problem sets.
Synopsis: The course will develop the classical theory of symmetric functions from a combinatorial perspective. Topics include Young tableaux, related combinatorial algorithms, and enumeration problems, as well as applications to representation theory of symmetric groups and Schubert calculus on Grassmannians.
Text:
[EC2] | R.P.Stanley, Enumerative combinatorics, vol.2, Cambridge University Press, 1999 (paperback 2001). |
We will cover Chapter 7 (including Appendix 1). |
Contents of Chapter 7:
Reference texts:
[Fu] | W.Fulton, Young tableaux , Cambridge University Press, 1997. |
[Ma] | I.G.Macdonald, Symmetric functions and Hall polynomials, 2nd edition, Oxford University Press, 1995 (paperback 1999). |
[Sa] | B.E.Sagan, The symmetric group, 2nd edition, Springer-Verlag, 2001. |
[EC1] | R.P.Stanley, Enumerative combinatorics, vol.1, 2nd edition, Cambridge University Press, 1997 (paperback 2000). |