Integer Cantor Sets: Arithmetic Combinatorial Properties

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Alex Burgin, Anastasios Fragkos, Michael Thoreau Lacey, Darío Mena, María Carmen Reguera
DOI: 10.48550/arxiv.2602.15292
Cited by: 0

Abstract

Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective property with power savings (b) characterize uniform distribution, (c) establish polynomial mean ergodic theorems and (d) study metric pair correlation of Cantor sets.

Fields of Study & Subjects

Analytic Number Theory Research Mathematical Dynamics and Fractals Limits and Structures in Graph Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
17 February 2026
Language
EN
Document type
Preprint