标题： 仿射半群的因式分解长度分布 V：数值半群上加权因式分解长度的显式渐近行为 显示英文标题

标题： Factorization length distribution for affine semigroups V: explicit asymptotic behavior of weighted factorization lengths on numerical semigroups

摘要： 我们描述了数值半群上加权分解长度的渐近行为。 我们的方法是几何的，而非分析的，解释了Curry-Schoenberg B样条作为极限分布的出现，并提供了显式的误差界（没有未指定的隐含常数）。 在此过程中，我们显式地界定了向量分拆函数与变量多面体中整数点数量之间的差异，其中矩阵为$2 \times k$。 显示英文摘要

摘要： We describe the asymptotic behavior of weighted factorization lengths on numerical semigroups. Our approach is geometric as opposed to analytic, explains the presence of Curry-Schoenberg B-splines as limiting distributions, and provides explicit error bounds (no implied constants left unspecified). Along the way, we explicitly bound the difference between the vector partition function and the number of integer points in the variable polytope for a $2 \times k$ matrix.