For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases 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), probability theory (weak convergence of measures, characteristic functions), and harmonic analysis (Fourier transforms of distributions). We provide instructive examples which demonstrate the power and generality of our techniques. We also highlight unexpected consequences in the theory of homogeneous symmetric functions.

对于具有指定生成器列表（不一定是最小生成器）的数值半群，对于所有主要分解长度统计，我们获得显式渐近表达式，在某些情况下为拟多项式/拟表示。这涉及本主题中不标准的各种工具，例如代数组合（舒尔多项式），概率论（度量的弱收敛，特征函数）和谐波分析（分布的傅立叶变换）。我们提供具有指导意义的示例，这些示例演示了我们技术的力量和普遍性。我们还强调了齐次对称函数理论中的意外结果。