  We prove that there is an algorithm to compute the class of the intersection
of the divisor of schemes incident to a fixed line with any other class of a
basis of the Chow ring $A^*(\mathbb{P}^{2[N]})$ due to Mallavibarrena and Sols.
This is progress towards a combinatorial description of the intersection
product on the Hilbert scheme of points in the projective plane.
