Enumeration of hypermaps and Hirota equations for extended rationally constrained KP

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-07 DOI:10.4310/cntp.2023.v17.n3.a3

G. Carlet, J. van de Leur, H. Posthuma, S. Shadrin

引用次数: 2

Abstract

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.

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扩展合理约束KP的超映射和Hirota方程的计数

我们考虑Riemann球面上亚纯函数空间上的Hurwitz-Dubrovin–Frobenius流形结构，该空间恰好具有两个极点，一个极点是简单的，一个是任意阶的。我们证明了与该Dubrovin–Frobenius流形相关的所有属配分函数（也称为全后代势）是Kadomtsev–Petviashvili层次的有理约简的tau函数。这个说法是刘、张和周推测出来的。我们还为这个将一组特定的时间与根超映射的枚举相关联的分区函数提供了部分枚举意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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