Résumé | Recently, residue and quotient tables were defined, and were used to describe strong covers in the lattice of k-bounded partitions. In the talk, we will show how residue and quotient tables can be used to describe many other results in the theory of k-bounded partitions and k-Schur functions, including k-conjugates, weak horizontal and vertical strips, and the k-Murnaghan-Nakayama rule. If time permits, evidence will be presented for the claim that one of the most important open questions in the theory of k-Schur functions, a general rule that would describe their product, can also be concisely stated in terms of residue tables. |