Subsum Sets: Intervals, Cantor Sets, and Cantorvals

Abstract

Given a sequence converging to zero, we consider the set of numbers which are sums of (infinite, finite, or empty) subsequences. When the original sequence is not absolutely summable, the subsum set is an unbounded closed interval which includes zero. When it is absolutely summable the subsum set is one of the following: a finite union of (nontrivial) compact intervals, a Cantor set, or a "symmetric Cantorval".

24 pages, 2 figures; replaces previous version (1106.3779) with different title (The subsum set of a null sequence), rewritten to shorten and take account of results not included in earlier version

Cited by in corpus (2)

• Levy-Steinitz theorem and achievement sets of conditionally convergent series on the real plane
• Subsums of Null Sequences: A Survey and Open Questions