Generating stable modular graphs

We present and prove the correctness of the program boundary, whose sources are available at http://people.sissa.it/~maggiolo/boundary/. Given two natural numbers g and n satisfying 2g+n−2>0, the program generates all genus g stable graphs with nunordered marked points. Each such graph determines the topological type of a nodal stable curve of arithmetic genus g with n unordered marked points. Our motivation comes from the fact that the boundary of the moduli space of stable genus g, n-pointed curves can be stratified by taking loci of curves of a fixed topological type.