单连通渗漏完备Hurwitz数的拟多项式性与N点函数
Quasi-polynomiality and $N$-point functions of single connected leaky completed Hurwitz numbers
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中文总结 AI 辅助
本文研究单连通渗漏完备Hurwitz数的结构，证明其拟多项式性并给出生成函数闭式公式，为研究渗漏Hurwitz数的亏格依赖性提供了工具。
中文摘要 AI 辅助
本文研究单连通k渗漏(r+1)完备Hurwitz数的结构。首先证明，对于固定亏格，提取显式Pochhammer型因子乘积后，分划μ对应的稳定连通渗漏Hurwitz数是商[μ_i]模k+r的多项式。随后给出单连通渗漏Hurwitz数生成函数的闭式公式，可用于研究渗漏Hurwitz数的亏格依赖性。
英文摘要
In this paper, we study the structures of single connected $k$-leaky $(r+1)$-completed Hurwitz numbers. We first prove that, for fixed genus, after extracting an explicit product of Pochhammer type factors, the stable connected leaky Hurwitz numbers for partition $μ$ are polynomials in the quotients $[μ_i]$ modulo $k+r$. We then give a closed formula for the generating function of single connected leaky Hurwitz numbers, which can be used to study the genus dependence of leaky Hurwitz numbers.
