Results and conjectures on the number of standard strong marked tableaux

Many results involving Schur functions have analogues involving k-Schur functions. Standard strong marked tableaux play a role for k-Schur functions similar to the role standard Young tableaux play for Schur functions. We discuss results and conjectures toward an analogue of the hook-length formula.New tools, residue and quotient tables, are presented, which allow for efficient computation of strong covers and have the potential to describe many other phenomena in k-function theory.