Equivariant Hodge polynomials of heavy/light moduli spaces

Let ${\bar{\mathcal{M}}}_{g,m\mathrm{\mid }n}$ denote Hassett’s moduli space of weighted pointed stable curves of genus $g$ for the heavy/light weight data $(1^{(m)},1\mathrm{/}{n}^{(n)})$, and let ${\mathcal{M}}_{g,m\mathrm{\mid }n}\subset {\bar{\mathcal{M}}}_{g,m\mathrm{\mid }n}$ be the locus parameterizing smooth, not necessarily distinctly marked curves. We give a change-of-variables formula which computes the generating function for $(S_m\times S_n)$-equivariant Hodge-Deligne polynomials of these spaces in terms of the generating functions for $S_n$-equivariant Hodge-Deligne polynomials of ${\bar{\mathcal{M}}}_{g,n}$ and ${\mathcal{M}}_{g,n}$.