Counting Cubic Maps with Large Genus

Z. Gao, M. Kang

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

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
Land/GebietÖsterreich
OrtVirtuell
Zeitraum15/06/2019/06/20

ASJC Scopus subject areas

  • Software

Fields of Expertise

  • Information, Communication & Computing

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