FINITE PATTERN PROBLEMS RELATED TO LUROTH EXPANSION

作者：Tian, Zhigang; Wu, Min; Lou, Man-Li^*

来源：Fractals, 2020, 28(3): 2050048.

DOI：10.1142/S0218348X20500486

• Luroth Expansion
• Finite Pattern
• Hausdorff Dimension

Let F be a set of countable many functions, where every function f is an element of F satisfies f : Z -> Z and f (n) -> +infinity as n -> +infinity. This paper studies the size of the set consisting of those numbers whose Luroth digit sequence is strictly increasing and contains any finite pattern of F. We prove that the Hausdorff dimension of such set is 1/2 and give several applications.

• 单位
  广东技术师范学院