Thom polynomials and Schur funcions: the singularities $A_3(-)$

Combining the "method of restriction equations" of Rim\'anyi et al. with the techniques of symmetric functions, we establish the Schur function expansions of the Thom polynomials for the Morin singularities $A_3: ({\bf C}^{\bullet},0)\to ({\bf C}^{\bullet + k},0)$ for any nonnegative integer $k$.