Enumeration of hypermaps and Hirota equations for extended rationally constrained KP

DOI10.4310/CNTP.2023.V17.N3.A3zbMath1529.14018arXiv2211.12259OpenAlexW4309873800MaRDI QIDQ6069442

Hessel Posthuma, Sergey Shadrin, Guido Carlet, Johan W. van de Leur

Publication date: 14 November 2023

Published in: Communications in Number Theory and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.12259

zbMATH Keywords

Hirota equationsFrobenius manifoldsLax equationsKadomtsev-Petviashvili hierarchyenumeration of hypermaps

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Enumeration in graph theory (05C30) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45) Relationships between algebraic curves and physics (14H81)

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The constrained KP hierarchy and the bigraded Toda hierarchy of \((M, 1)\)-type ⋮ Dubrovin–Frobenius manifold structures on the orbit space of the symmetric group

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