Dimensions of the perturbed Cantor set (Q1322641)

A perturbed Cantor set \(F\) is determined from two sequences \(\{a_ n\}\) and \(\{b_ n\}\) such that if \(I_{n,1}\), \(I_ n\) and \(I_{n,2}\) are the left, the midle, and the right intervals (respectively) in the \(n\)th generation of a triadic decomposition of \([0,1]\) we have \(| I_{n,1}|/| I_ n|= a_ n\) and \(| I_{n,2}|/| I_ n|= b_ n\), provided that \(\inf(1- a_ n- b_ n)>0\). The author examines the relation between Hausdorff dimension and packing dimension [see \textit{K. J. Falconer}, ``Fractal geometry: mathematical foundations and applications (1990; Zbl 0689.28003)] for the class of permuted Cantor sets.