Algebraic Combinatorics 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. Recommended books
- 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”.