A pattern for the asymptotic number of rooted maps on surfaces

DOI10.1016/0097-3165(93)90097-RzbMath0792.05073MaRDI QIDQ1318367

Zhi-Cheng Gao

Publication date: 24 July 1994

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

zbMATH Keywords

surfacepatternrooted mapssmooth maps

Mathematics Subject Classification ID

Enumeration in graph theory (05C30)

Related Items (17)

Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials ⋮ Schnyder woods for higher genus triangulated surfaces, with applications to encoding ⋮ Enumeration of cubic multigraphs on orientable surfaces ⋮ Almost all rooted maps have large representativity ⋮ Phase diagram and topological expansion in the complex quartic random matrix model ⋮ An arithmetic property of moments of the \(\beta\)-Hermite ensemble and certain map enumerators ⋮ Cubic graphs and related triangulations on orientable surfaces ⋮ A bijection for nonorientable general maps ⋮ Random graphs on surfaces ⋮ On the Asymptotic Number of Plane Curves and Alternating Knots ⋮ Universality and asymptotics of graph counting problems in non-orientable surfaces ⋮ 0-1 laws for maps ⋮ Distributions of near-4-regular maps on the sphere and the projective plane ⋮ Exact enumeration of rooted 3-connected triangular maps on the projective plane ⋮ Minimum weight disk triangulations and fillings ⋮ A pattern of asymptotic vertex valency distributions in planar maps ⋮ Description trees and Tutte formulas.

Cites Work

• A survey of the asymptotic behaviour of maps
• 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)
• The asymptotic number of rooted nonseparable maps on a surface
• The number of rooted triangular maps on a surface
• The number of rooted 2-connected triangular maps on the projective plane
• The asymptotic number of rooted 2-connected triangular maps on a surface
• Submaps of maps. I: General 0-1 laws
• Submaps of maps. II: Cyclically \(k\)-connected planar cubic maps
• Counting rooted maps by genus. III: Nonseparable maps
• The number of degree restricted maps on general surfaces
• Counting rooted maps by genus. I
• A Census of Planar Triangulations
• Asymptotic Methods in Enumeration
• Almost all rooted maps have large representativity
• A Character Theoretic Approach to Embeddings of Rooted Maps in an Orientable Surface of Given Genus
• Character Theory and Rooted Maps in an Orientable Surface of Given Genus: Face-Colored Maps
• The Enumeration of Maps on the Torus and the Projective Plane
• On the enumeration of non-planar maps
• On the enumeration of planar maps
• A Census of Planar Maps
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