Factorization length distribution for affine semigroups II: asymptotic behavior for numerical semigroups with arbitrarily many generators

Abstract

For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions or quasipolynomial/quasirational representations for all major factorization length statistics. This involves a variety of tools that are not standard in the subject, such as algebraic combinatorics (Schur polynomials and the Jacobi-Trudi formula), probability theory (weak convergence of measures, characteristic functions), and Fourier transforms of distributions. We also provide instructive examples to demonstrate the power and generality of our techniques.