{"title":"The Number of Double Triangles in Random Planar Maps","authors":"M. Drmota, Guanglong Yu","doi":"10.4230/LIPIcs.AofA.2018.19","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":175372,"journal":{"name":"International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.AofA.2018.19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
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.
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