标题： 简单Hurwitz数和变亏格的单调Hurwitz数的结构 显示英文标题

标题： The structures of simple Hurwitz numbers and monotone Hurwitz numbers with varying genus

摘要： 我们研究了普通简单Hurwitz数和变亏格的单调Hurwitz数的结构。 更准确地说，我们证明当分支类型固定而亏格被视为变量时，连通的单调Hurwitz数是指数函数和多项式的乘积的线性组合，而普通简单Hurwitz数是指数函数的线性组合。 利用这些结构性质，我们还推导了这两种Hurwitz数的大亏格渐进行为。 作为结果，我们证明了一个猜想，并反驳了另一个猜想，这两个猜想均由Do、He和Robertson提出。 显示英文摘要

摘要： We study the structures of ordinary simple Hurwitz numbers and monotone Hurwitz numbers with varying genus. More precisely, we prove that when the ramification type is fixed and the genus is treated as a variable, the connected monotone Hurwitz number is a linear combination of products of exponentials and polynomials, and the ordinary simple Hurwitz number is a linear combination of exponentials. Using these structural properties, we also derive the large genus asymptotics of these two kinds of Hurwitz numbers. As a result, we prove one conjecture, and disprove another, both proposed by Do, He and Robertson.