## 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.
#### Topics

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