18.315 Combinatorial Theory

Topic for fall 1996: symmetric functions.

Course meets: Tuesdays and Thursdays, 1-2:30, Room 4-145.

Lecturer: Professor Sergey Fomin, Room 2-363B, 253-1713, fomin@math.mit.edu

Text: R.P.Stanley, Enumerative combinatorics, vol.2, to appear circa 1998.

Reference texts:

  • I.G.Macdonald, Symmetric functions and Hall polynomials, 2nd edition, Oxford University Press, 1995.
  • B.E.Sagan, The symmetric group, Wadsworth and Brooks/Cole, 1991.
  • R.P.Stanley, Enumerative combinatorics, vol.1, Wadsworth and Brooks/Cole, 1986. Second edition to be published by Oxford University Press.


  • The ring of symmetric functions and its various bases. The Schur functions
  • Identities involving symmetric functions
  • Young tableaux. The Robinson-Schensted-Knuth correspondence
  • Noncommutative Schur functions
  • The Littlewood-Richardson and Murnaghan-Nakayama rules
  • Irreducible representations of the symmetric group. The Frobenius map
  • Enumeration of plane partitions
  • Quasi-symmetric functions. Ribbon Schur functions
  • "Jeu de taquin." Knuth equivalence. Greene's invariants.

    Homework #1
    Homework #2
    Homework #3

    Course description from the MIT Catalog