Integer Cantor Sets: Arithmetic Combinatorial Properties

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.