  Vector-valued Jack polynomials associated to the symmetric group ${\mathfrak
S}_N$ are polynomials with multiplicities in an irreducible module of
${\mathfrak S}_N$ and which are simultaneous eigenfunctions of the
Cherednik-Dunkl operators with some additional properties concerning the
leading monomial. These polynomials were introduced by Griffeth in the general
setting of the complex reflections groups $G(r,p,N)$ and studied by one of the
authors (C. Dunkl) in the specialization $r=p=1$ (i.e. for the symmetric
group). By adapting a construction due to Lascoux, we describe an algorithm
allowing us to compute explicitly the Jack polynomials following a Yang-Baxter
graph. We recover some properties already studied by C. Dunkl and restate them
in terms of graphs together with additional new results. In particular, we
investigate normalization, symmetrization and antisymmetrization, polynomials
with minimal degree, restriction etc. We give also a shifted version of the
construction and we discuss vanishing properties of the associated polynomials.
