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math.CA2026
New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions
Richárd Balka, Tamás Keleti
We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that…
math.CA2025
Signed null sequences and Hausdorff dimension
Richárd Balka, Kornélia Héra, Gergely Kiss
We investigate the convergence of signed null sequences of the form \[ \sum_{n=1}^\infty \varepsilon_n a_n, \quad \varepsilon_n \in \{-1,1\}, \] where tends to zero in $\ma…