Augmented monomial symmetric polynomial for a partition and variable list
AugmentedSymmetricPolynomial[{r1, r2, …}]
AugmentedSymmetricPolynomial[{{r11, …, r 1n}, {r21, …, r 2n}, …}]
AugmentedSymmetricPolynomial[rspec, data]
AugmentedSymmetricPolynomial[{1, 2}, {x, y, z}]
→ x^2*y + x*y^2 + x^2*z + y^2*z + x*z^2 + y*z^2