he quasisymmetrics in superspace are the invariants under hivert action when acting diagonally on commuting and anticommuting variables. By equipping the superspace with a bilinear form using partial derivative operators, the harmonics are the orthogonal complement of the ideal generated by nontrivial quasisymmetrics. The harmonics of the polynomial ring in commuting variables was counted by catalan numbers and then a basis indexed by "indexed forests" was given. An indexed forest is a sequence of binary rooted trees and the leaves is a noncrossing and nonnested partition.

I will speak about some polarization operator that map the harmonics of the polynomial ring into harmonics of the superspace. We will see they are indexed by sets of marked binary rooted trees in which the set of leaves is a noncrossing partition.