Explicit closed algebraic formulas for Orlov-Scherbin \(n\)-point functions

DOI10.5802/jep.202zbMath1504.37080arXiv2008.13123OpenAlexW4285083679WikidataQ113689211 ScholiaQ113689211MaRDI QIDQ2154281

Maxim E. Kazaryan, Sergey Shadrin, B. S. Bychkov, P. I. Dunin-Barkowski

Publication date: 19 July 2022

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.13123

zbMATH Keywords

Fock spaceHurwitz numbersKP tau functions

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) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Coverings of curves, fundamental group (14H30) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items

2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula ⋮ Diagonal tau-functions of 2d Toda lattice hierarchy, connected \((n,m)\)-point functions, and double Hurwitz numbers ⋮ Generalised ordinary vs fully simple duality for \(n\)-point functions and a proof of the Borot-Garcia-Failde conjecture ⋮ A simple formula for the \(x\)-\(y\) symplectic transformation in topological recursion ⋮ Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewański conjecture ⋮ Grothendieck’s dessins d’enfants in a web of dualities. III

Cites Work

• Unnamed Item
• Unnamed Item
• Hypergeometric solutions of soliton equations
• Ramifications of Hurwitz theory, KP integrability and quantum curves
• Fermionic approach to weighted Hurwitz numbers and topological recursion
• Weighted Hurwitz numbers and topological recursion
• Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants
• Simple maps, Hurwitz numbers, and topological recursion
• Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion
• Combinatorial structure of colored HOMFLY-PT polynomials for torus knots
• Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula
• Virasoro constraints and topological recursion for Grothendieck's dessin counting
• GENERALIZED KAZAKOV-MIGDAL-KONTSEVICH MODEL: GROUP THEORY ASPECTS
• Weighted Hurwitz numbers and hypergeometric $\tau$-functions: an overview
• On double Hurwitz numbers with completed cycles
• Combinatorial solutions to integrable hierarchies
• Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson–Pandharipande–Tseng formula
• Asymptotic Enumeration of Constellations and Related Families of Maps on Orientable Surfaces
• Weighted Hurwitz numbers and topological recursion: An overview
• Towards an orbifold generalization of Zvonkine’s 𝑟-ELSV formula
• Blobbed topological recursion: properties and applications
• Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation

This page was built for publication: Explicit closed algebraic formulas for Orlov-Scherbin \(n\)-point functions