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- W4315779780 abstract "We present a procedure to sample uniformly from the set of combinatorial isomorphism types of balanced triangulations of surfaces — also known as graph-encoded surfaces. For a given number n, the sample is a weighted set of graph-encoded surfaces with 2n triangles.The sampling procedure relies on connections between graph-encoded surfaces and permutations, and basic properties of the symmetric group.We implement our method and present a number of experimental findings based on the analysis of 138 million runs of our sampling procedure, producing graph-encoded surfaces with up to 280 triangles.Namely, we determine that, for n fixed, the empirical mean genus of our sample is very close to . Moreover, we present experimental evidence that the associated genus distribution more and more concentrates on a vanishing portion of all possible genera as n tends to infinity. Finally, we observe from our data that the mean number of non-trivial symmetries of a uniformly chosen graph encoding of a surface decays to zero at a rate super-exponential in n." @default.
- W4315779780 created "2023-01-13" @default.
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- W4315779780 date "2023-01-01" @default.
- W4315779780 modified "2023-10-04" @default.
- W4315779780 title "A Uniform Sampling Procedure for Abstract Triangulations of Surfaces" @default.
- W4315779780 doi "https://doi.org/10.1137/1.9781611977561.ch2" @default.
- W4315779780 hasPublicationYear "2023" @default.
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