Intersections of $\omega$ classes in $\overline{\mathcal{M}}_{g,n}$

Abstract

We provide a graph formula which describes an arbitrary monomial in {\omega} classes (also referred to as stable {\psi} classes) in terms of a simple family of dual graphs (pinwheel graphs) with edges decorated by rational functions in {\psi} classes. We deduce some numerical consequences and in particular a combinatorial formula expressing top intersections of \k{appa} classes on Mg in terms of top intersections of {\psi} classes.