Can you determine a set of values from a set of sums?

No: both $(1, 1, 2, 2)$ and $(1, 1, 1, 3)$ give you the set $\{1, 2, 3, 4, 5, 6\}$.


The answer is no.

Take the following subvectors:

$$A = (1, 1, 3)$$$$B = (1,2,2)$$It's easy to see that both vectors have a sum vector of $[1,2,3,4,5]$.

Tags:

Combinatorics

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