Enumeration of strong, standard, starred tableaux

Schur functions are a basis for the ring of symmetric functions, one with many important algebraic and combinatorial properties. k-Schur functions are a basis for a certain subring of that ring are turning out to be just as interesting. 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. I will discuss results and conjectures toward an analogue of the hook length formula. This is joint work with Matjaz Konvalinka.