Special Cases of the Orbifold Version of Zvonkine’s r-ELSV Formula

Abstract

We prove the orbifold version of Zvonkine’s r-ELSV formula in two special cases: the case of $\mathit{r}=2$ (completed 3-cycles) for any genus $\mathit{g}\ge 0$ and the case of any $\mathit{r}\ge 1$ for genus $\mathit{g}=0$.