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For numerical semigroups with a specified list of (not necessarily minimal)generators, we obtain explicit asymptotic expressions, and in some casesquasipolynomial/quasirational representations, for all major factorizationlength statistics. This involves a variety of tools that are not standard inthe subject, such as algebraic combinatorics (Schur polynomials), probabilitytheory (weak convergence of measures, characteristic functions), and harmonicanalysis (Fourier transforms of distributions). We provide instructive exampleswhich demonstrate the power and generality of our techniques. We also highlightunexpected consequences in the theory of homogeneous symmetric functions.

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