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Article Dans Une Revue Communications in Number Theory and Physics Année : 2023

Enumeration of hypermaps and Hirota equations for extended rationally constrained KP

Résumé

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.

Dates et versions

hal-04361482 , version 1 (22-12-2023)

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Citer

Guido Carlet, J. van de Leur, H. Posthuma, S. Shadrin. Enumeration of hypermaps and Hirota equations for extended rationally constrained KP. Communications in Number Theory and Physics, 2023, 17 (3), pp.643-708. ⟨10.4310/CNTP.2023.v17.n3.a3⟩. ⟨hal-04361482⟩
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