  We explain how to compute top-dimensional intersections of psi-classes on
moduli spaces of m-stable curves. On the moduli spaces of Deligne-Mumford
stable pointed curves of genus one, these intersection numbers are determined
by two recursions, namely the string equation and the dilaton equation. We
establish, for each integer m>0, an analogous pair of recursions which
determine these intersection numbers on the moduli spaces of m-stable pointed
curves of genus one.
