On the intersection of an m-part uniform Cantor set with its rational translation

Abstract

In this paper, we study an m-part uniform Cantor set with its rational translation. We give the fractal structure and the formula of the box-counting dimension of the intersection I( t). We find that the Hausdorff measures of these sets form a discrete spectrum whose non-zero values come only from translating the length t with its n-base expansion.