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Bounding the dimension of points on a line
Information and Computation ( IF 1 ) Pub Date : 2020-06-22 , DOI: 10.1016/j.ic.2020.104601
Neil Lutz , D.M. Stull

We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x,ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower bound on the (classical) Hausdorff dimension of generalized sets of Furstenberg type.



中文翻译:

界定线上点的尺寸

我们使用Kolmogorov复杂度方法来给出该点的有效Hausdorff维数的下界 X一种X+b给定实数abx。我们将主定理应用于分形几何问题,从而给出了Furstenberg类型广义集的(经典)Hausdorff维上的改进下界。

更新日期:2020-06-22
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