Alex Rutar

activity

20242026

collaborators

11 papers

math.NT2026

Multi-scale properties of continued fraction sets

Alex Rutar

We survey the dimension theory of sets of real numbers with regular continued fraction expansion restricted to a non-empty and possibly infinite subset $\mathcal{D}\subset\mathbb{N…

math.CO2026

Visible parts and lower bounds on point-ray incidences

Tuomas Orponen, Alex Rutar

Let $K \subset R^{2}$ be a compact set. For $I^¸ \in S^{1}$ , let $Vis_{I^} ¸ (K) \subset K$ be the visible part of $K$ in direction $I^¸$ . We prove that $\operatorname{di…

math.CA2026

Attainable forms of lower spectra

Amlan Banaji, Haipeng Chen, Alex Rutar +1

Let $d \in N$ and $I ¨ : (0, 1) \to [0, d]$ . We prove there exists a set $F \subset R^{d}$ whose lower spectrum $dim^{I^} ¸_{L} F$ satisfies $(1-Î¸)\o…

math.DS2025

Assouad spectrum of Gatzouras-Lalley carpets

Amlan Banaji, Jonathan M. Fraser, IstvÃ¡n KolossvÃ¡ry +1

We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum o…

math.MG2025

On the uniformity and size of microsets

RichÃ¡rd Balka, Vilma OrgovÃ¡nyi, Alex Rutar

We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set $K \subset R^{d}$ with Assouad dimen…

math.DS2025

Regularity of non-autonomous self-similar sets

Antti KÃ¤enmÃ¤ki, Alex Rutar

Non-autonomous self-similar sets are a family of compact sets which are, in some sense, highly homogeneous in space but highly inhomogeneous in scale. The main purpose of this note…