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- W4309201600 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 $bar{g}(n)$ of our sample is very close to $bar{g}(n) = frac{n-1}{2} - (16.98n -110.61)^{1/4}$. 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.
- W4309201600 created "2022-11-24" @default.
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- W4309201600 date "2022-11-14" @default.
- W4309201600 modified "2023-09-30" @default.
- W4309201600 title "A Uniform Sampling Procedure for Abstract Triangulations of Surfaces" @default.
- W4309201600 doi "https://doi.org/10.48550/arxiv.2211.07798" @default.
- W4309201600 hasPublicationYear "2022" @default.
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