subset sum


Sets with distinct subset sums ★★★

Author(s): Erdos

Say that a set $ S \subseteq {\mathbb Z} $ has distinct subset sums if distinct subsets of $ S $ have distinct sums.

Conjecture   There exists a fixed constant $ c $ so that $ |S| \le \log_2(n) + c $ whenever $ S \subseteq \{1,2,\ldots,n\} $ has distinct subset sums.

Keywords: subset sum

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