The algebra of symmetric functions, Schur functions, RSK algorithm, Murnaghan-
Nakayama Rule, Hillman-Grassl correspondence, Knuth equivalence, jeu de taquim,
promotion and evacuation, Littlewood-Richardson rules.
No prior knowledge of combinatorics is expected, but a familiarity with linear
algebra and finite groubs will be assumed.
Suggested books and references:
Stanley, R., Enumerative Combinatorics, volume 2
,Cambridge University Press, 2001.
Sagan, B., The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions
,Graduate Texts in Mathematics vol. 203, Springer-Verlag, 2001.
Prasad, A., Representation Theory : A Combinational Viewpoint
,Cambridge Studies in Advanced Mathematics vol. 147, 2014.
Stanley, R., Lecture notes on Topics in Algebraic Combinatorics
.