Sums of Cantor Sets yielding an Interval

CABRELLI, C.; HARE, K.; MOLTER, U.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS

Cambridge University Press

Año: 2002 vol. 73 p. 405 - 418

0263-6115

In this paper we prove that if a Cantor set has ratios of dissection boundedaway from zero, then there is a natural number $N$, such that its $N$-foldsum is an interval. Moreover, for each element $z$ of this interval, weexplicitly construct the $N$ elements of $C$ whose sum yields $z$. We alsoextend a result of Mendes and Oliveira showing that when $s$ is irrational $%C_{a}+C_{a^{s}}$ is an interval if and only if $\frac{a}{1-2a}\frac{a^s}{%1-2a^s} \geq 1$.