We consider the Hurwitz Dubrovin–Frobenius manifold structure on the space of meromorphic functions on the Riemann sphere with exactly two poles, one simple and one of arbitrary order. We prove that the all genera partition function (also known as the total descendant potential) associated with this Dubrovin–Frobenius manifold is a tau function of a rational reduction of the Kadomtsev–Petviashvili hierarchy. This statement was conjectured by Liu, Zhang, and Zhou. We also provide a partial enumerative meaning for this partition function associating one particular set of times with enumeration of rooted hypermaps.

中文翻译：

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扩展有理约束 KP 的超图和 Hirota 方程的枚举

我们考虑黎曼球上亚纯函数空间上的 Hurwitz Dubrovin-Frobenius 流形结构，该结构恰好有两个极点，一个是简单的，一个是任意阶的。我们证明与杜布罗文-弗罗贝尼乌斯流形相关的所有属分配函数（也称为总后代势）是 Kadomtsev-Petviashvili 层次结构有理约简的 tau 函数。这一说法是刘、张、周三人的猜测。我们还为该分区函数提供了部分枚举含义，将一组特定的时间与根超图的枚举相关联。