Combinatorial cycles on the moduli spaces of pointed stable curves

Let ${\overline{\cal M}}_{g,n}$ be the moduli space of $n$-pointed genus $g$ stable curves. The collection of `ribbon graphs' allows to define some combinatorial cycles on ${\overline{\cal M}}_{g,n}$. A Theorem of Di Francesco, Itzykson, and Zuber should yield explicit relations involving the above cycles. In this talk we discuss a technical aspect of this Theorem concerning the coefficients appearing in these relations.