The Littlewood-Richardson coefficients $c^\lambda_{\mu\nu}$ appear in the expansion of a product of Schur functions into Schur functions, $s_{\mu}(x)s_\nu(x)=\sum_\lambda c^\lambda_{\mu\nu}s_\lambda(x)$. There is a combinatorial rule for computing these coefficients.

Zonal polynomials are somewhat similar to Schur functions (both are particular cases of Jack polynomials and are related to representation theory). Is there a combinatorial rule for computing the analogues of the LR coefficients for zonal polynomials?

There is already a similar question (Littlewood-Richardson coefficients for Jack symmetric functions) for Jack polynomials, but I am interested in a specific and certainly simpler case.