Counting Cubic Maps with Large Genus

Z. Gao, M. Kang

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem Konferenzband

Abstract

We derive an asymptotic expression for the number of cubic maps on orientable surfaces when the genus is proportional to the number of vertices. Let Σ_g denote the orientable surface of genus g and θ=g/n∈ (0,1/2). Given g,n∈ ℕ with g→ ∞ and n/2-g→ ∞ as n→ ∞, the number C_{n,g} of cubic maps on Σ_g with 2n vertices satisfies C_{n,g} ∼ (g!)² α(θ) β(θ)ⁿ γ(θ)^{2g}, as g→ ∞, where α(θ),β(θ),γ(θ) are differentiable functions in (0,1/2). This also leads to the asymptotic number of triangulations (as the dual of cubic maps) with large genus. When g/n lies in a closed subinterval of (0,1/2), the asymptotic formula can be obtained using a local limit theorem. The saddle-point method is applied when g/n→ 0 or g/n→ 1/2.
Originalspracheenglisch
Titel31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Redakteure/-innenMichael Drmota, Clemens Heuberger
ErscheinungsortSaarbrücken/Wadern
Herausgeber (Verlag)Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH
Seitenumfang13
ISBN (elektronisch)9783959771474
ISBN (Print)18688969
DOIs
PublikationsstatusVeröffentlicht - 2020
Veranstaltung31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - https://www.math.aau.at/AofA2020/, Virtuell, Österreich
Dauer: 15 Jun 202019 Jun 2020

Publikationsreihe

NameLeibniz International Proceedings in Informatics, LIPIcs
Band159

Konferenz

Konferenz31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
KurztitelAofA2020
LandÖsterreich
OrtVirtuell
Zeitraum15/06/2019/06/20

ASJC Scopus subject areas

  • Software

Fields of Expertise

  • Information, Communication & Computing

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