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Sums of Cantor sets yielding an interval
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 73 / Issue 3 / December 2002
- Published online by Cambridge University Press:
- 09 April 2009, pp. 405-418
- Print publication:
- December 2002
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- Article
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In this paper we prove that if a Cantor set has ratios of dissection bounded away from zero, then there is a natural number N, such that its N-fold sum is an interval. Moreover, for each element z of this interval, we explicitly construct the N elements of C whose sum yields z. We also extend a result of Mendes and Oliveria showing that when s is irrational
is an interval if and only if a /(1−2a) as/(1−2as) ≥ 1.
is an interval if and only if a /(1−2