A Combinatorial Formula for Monomials in Kontsevich’s Ψ-Classes

Diagonal complexes provide a simplicial model for Kontsevich’s tautological bundles over Mg,n. The local combinatorial formula for the first Chern class yields a combinatorial formula for the ψ-classes (that is, the first Chern classes of the tautological bundles). In the present paper, we derive a formula for arbitrary monomials in ψ-classes.