A. Rutar

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math.CA2025

Interpolating with generalized Assouad dimensions

Amlan Banaji, Alex Rutar, Sascha Troscheit

The $I ¨ $ -Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectru…

math.CA2024

Attainable forms of Assouad spectra

Alex Rutar

Let $d \in N$ and let $I ¨ : (0, 1) \to [0, d]$ . We prove that there exists a set $F \subset R^{d}$ such that $dim_{A}^{I^} ¸ F = I ¨ (I^¸)$ for all $I^¸ \in (0, 1)$ if an…