Two divisibility problems on subset sums

Konstantinos Gaitanas

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arXiv · 1911.11097

Two divisibility problems on subset sums

Konstantinos Gaitanas

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Abstract

We consider two problems regarding some divisibility properties of the subset sums of a set $A\subseteq \{1, 2, \ldots ,n\}$. At the beginning, we study the cardinality of $A$ which has the following property: For every $d\le n$ there is a non empty set $A_d\subseteq A$ such that the sum of the elements of $A_d$ is a multiple of $d$. Next, we turn our attention to another problem: If all subset sums of $A$ form a multiple free-sequence, what can we say about the structure of $A$? We give some asymptotics for the first problem and improve some already existing results for the second one.

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BibTeX RIS

Konstantinos Gaitanas. 2019-11-25. Two divisibility problems on subset sums. https://arxiv.org/abs/1911.11097

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