The Number of Double Triangles in Random Planar Maps

Authors Michael Drmota , Guan-Ru Yu

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Author Details

Michael Drmota
  • TU Wien, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8--10, 1040 Vienna, Austria
Guan-Ru Yu
  • TU Wien, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8--10, 1040 Vienna, Austria

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Michael Drmota and Guan-Ru Yu. The Number of Double Triangles in Random Planar Maps. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The purpose of this paper is to provide a central limit theorem for the number of occurrences of double triangles in random planar maps. This is the first result of this kind that goes beyond face counts of given valency. The method is based on generating functions, an involved combinatorial decomposition scheme that leads to a system of catalytic functional equations and an analytic extension of the Quadratic Method to systems of equations.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Graph enumeration
  • Planar maps
  • pattern occuence
  • generating functions
  • quadratic method
  • central limit theorem


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