Presentation of students' mini-projects:

- Plethysm of symmetric functions. 

   Expansion of the plethysm of complete symmetric functions, and of the plethysm of complete symmetric functions and powers sums as linear combinations of Schur functions.

- Representations of permutation group S_n:  Specht modules

    Irreducible complex finite-dimensional representations of a symmetric group.

    Classes of conjugation of a symmetric group S_n: isomorphism with the partitions of n.

    Group ring C[S_n].

     Definition and properties of Specht modules S^{\lambda}.

Robinson-Schensted-Knuth correspondence, and its properties.

Row insertion algorithm for semi-standard Young tableaux.

Bruhat order on symmetric group, and Schubert polynomials.

Divided difference operator on the ring of polynomials.

Character theory.

Particular case of symmetric group.