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Counting elements and geodesics in Thompson's group F

Elder, Murray and Fusy, Éric and Rechnitzer, Andrew (2010) Counting elements and geodesics in Thompson's group F. Journal of Algebra, 324 (1). pp. 102-121. ISSN 00218693

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    Abstract

    We present two quite different algorithms to compute the number of elements in the sphere of radius n of Thompson’s group F with standard generating set. The first of these requires exponential time and polynomial space, but additionally computes the number of geodesics and is generalisable to many other groups. The second algorithm requires polynomial time and space and allows us to compute the size of the spheres of radius n with n ≤ 1500. Using the resulting series data we find that the growth rate of the group is bounded above by 2.62167 . . .. This is very close to Guba’s lower bound of (3+√5)/2. Indeed, numerical analysis of the series data strongly suggests that the growth rate of the group is exactly (3+√5)/2 .

    Item Type: Article
    Subjects: 05-xx Combinatorics > 05Axx Enumerative combinatorics
    20-xx Group theory and generalizations
    Faculty: UNSPECIFIED
    Depositing User: Dr Murray Elder
    Date Deposited: 17 Sep 2012 10:41
    Last Modified: 17 Sep 2012 10:41
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1065

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