Abstract
Let [Formula: see text] and [Formula: see text] an integer. We consider the collection [Formula: see text] of homogeneous self-similar sets on the line such that every two of copies [Formula: see text] of the self-similar set [Formula: see text] are either separated or overlapped with rank [Formula: see text] in [Formula: see text]. For [Formula: see text] generated by [Formula: see text] similitudes, we denote by [Formula: see text] the number of overlaps with rank [Formula: see text]. The set of points in the self-similar set having a unique coding is called the univoque set and denoted by [Formula: see text]. In this paper, we investigate a uniform method to calculate the Hausdorff dimension of the set [Formula: see text].
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