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An example would be $\{1, 3, 7\}$, which has subsets with sums $1, 3, 7, 4, 10, 8, 11$.

What is this called?

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    $\begingroup$ I don't know of a special name, but here is a reference. $\endgroup$ – vadim123 Jul 27 '14 at 19:31
  • $\begingroup$ @amWhy thanks, I edited. $\endgroup$ – 1.618 Jul 27 '14 at 19:40
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    $\begingroup$ If one only demands that the pairwise sums are distinct, then this would be a Sidon set. But I know that doesn't answer your question. $\endgroup$ – Greg Martin Jul 27 '14 at 20:05
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They are usually called sets with distinct subset sums. The name is a little long, but is self-descriptive, which is a plus. Sometimes it gets shortened to subset-sum-distinct set, or SSD-set. Like in the paper On subset-sum-distinct sequences by Jaegug Bae.

ssd

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