Non-recursive counts of graphs on surfaces

DOI10.54550/eca2023v3s3r20MaRDI QIDQ6659959

Brandon Tippings, Joceline C. Lega, Nicholas M. Ercolani

Publication date: 9 January 2025

Published in: Enumerative Combinatorics and Applications (Search for Journal in Brave)

zbMATH Keywords

hypergeometric functionstransfer matricesmap enumerationanalytical combinatorics

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Classical hypergeometric functions, ({}_2F_1) (33C05) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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• The continuum limit of Toda lattices for random matrices with odd weights
• Planar maps and continued fractions
• Random matrices, graphical enumeration and the continuum limit of Toda lattices
• Counting surfaces. CRM Aisenstadt chair lectures
• The asymptotic number of rooted maps on a surface
• Relations fonctionnelles et dénombrement des cartes pointées sur le tore. (Functional relations and the enumeration of rooted genus one maps)
• Topological quantum field theory
• Quantum field theory techniques in graphical enumeration
• The Euler characteristic of the moduli space of curves
• Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight \(\rho\)
• Matrix model calculations beyond the spherical limit.
• JT gravity and the ensembles of random matrix theory
• Growth of the number of simple closed geodesics on hyperbolic surfaces
• Caustics, counting maps and semi-classical asymptotics
• Conservation Laws of Random Matrix Theory
• A Bijection for Rooted Maps on Orientable Surfaces
• Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials
• Topological Expansion in the Cubic Random Matrix Model
• On the enumeration of non-planar maps
• On the enumeration of planar maps
• Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation
• Multiple scale asymptotics of map enumeration

Related Items (1)

Map enumeration from a dynamical perspective

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