Gap sequences of McMullen sets

Miao, Jun Jie; Xi, Li-Feng; Xiong, Ying

doi:10.1090/proc/13342

Gap sequences of McMullen sets
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by Jun Jie Miao, Li-Feng Xi and Ying Xiong PDF

Proc. Amer. Math. Soc. 145 (2017), 1629-1637 Request permission

Abstract:

We study the gap sequence of totally disconnected McMullen sets. Our result shows that if every horizontal line in the McMullen set is nonempty, then the gap sequence is unrelated to the box dimension. This implies that in such situations, the separation properties of McMullen sets are quite different from that of self-similar sets.

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