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arXiv · 2107.07885

Variations on the Erdős distinct-sums problem

Simone Costa·Marco Dalai·Stefano Della Fiore
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Abstract

Let $\{a_1, . . . , a_n\}$ be a set of positive integers with $a_1 < \dots < a_n$ such that all $2^n$ subset sums are distinct. A famous conjecture by Erdős states that $a_n>c\cdot 2^n$ for some constant $c$, while the best result known to date is of the form $a_n>c\cdot 2^n/\sqrt{n}$. In this paper, we weaken the condition by requiring that only sums corresponding to subsets of size smaller than or equal to $λn$ be distinct. For this case, we derive lower and upper bounds on the smallest possible value of $a_n$.

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Simone Costa, Marco Dalai, Stefano Della Fiore. 2022-10-28. Variations on the Erdős distinct-sums problem. https://arxiv.org/abs/2107.07885

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