Thom polynomials and Schur functions I

We give the Thom polynomials for the singularities I_2,2 and A_3 associated with maps (C^n,0) -> (C^{n+k},0) with parameter k>=0. We give the Schur function expansions of these Thom polynomials. Moreover, for the singularities A_i (with any parameter k >= 0) we analyze the ``first approximation'' F^(i) to the Thom polynomial. Our computations combine the characterization of Thom polynomials via the ``method of restriction equations'' of Rimanyi et al. with the techniques of (super) Schur functions.