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Discrete intermediate dimensions: endpoints, spectra and quasi-isometric invariance
Jinjun Li, Lifeng Xi, Shuqin Zhang
We introduce upper and lower discrete intermediate dimensions for unbounded subsets of Euclidean space and extend them to metric spaces. The definitions restrict the covering radii…
Projection theorems for macroscopic intermediate dimensions
Jinjun Li, Lifeng Xi
We introduce lower and upper macroscopic intermediate dimensions of unbounded subsets of Euclidean space by combining covering contributions from all dyadic annuli beyond a given s…
Spectrality of factors of product spectral measures
Mihail N. Kolountzakis, Chun-Kit Lai, Kailing Lai +1
We refine the method by Greenfeld and Lev for the product spectral set problem and generalize the theorem to a singular measure setting. Furthermore, we establish a new class of sp…
On Assouad dimension and arithmetic progressions in sets defined by digit restrictions
Jinjun Li, Min Wu, Ying Xiong
We show that the set defined by digit restrictions contains arbitrarily long arithmetic progressions if and only if its Assouad dimension is one. Moreover, we show that for any $0\…