Subsum Sets: Intervals, Cantor Sets, and Cantorvals
classification
🧮 math.HO
math.CAmath.GN
keywords
subsumabsolutelycantorfiniteintervalssequencesetssummable
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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".
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Cited by 1 Pith paper
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the center of distances for some multigeometric series
Provides a new sufficient condition for centers of distances of fast convergent series subsums and a complete description for certain multigeometric series as the union of centers for their n-initial subsums.
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