Stability versions of the inverse theorem for subset sums are proved: n-element positive real sets with at most binom(n+1,2)+1+M subset sums are characterized for M up to n-4, and sets with O(n^2) subset sums are characterized up to constants.
A structure theorem for sets with doubling $4+\delta$
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abstract
We prove a structural result for sets of integers with doubling at most $4 + \delta$, with $\delta>0$ sufficiently small. This generalises earlier work of Eberhard--Green--Manners which dealt with sets of integers with doubling strictly less than $4$, and makes progress towards a question of Green.
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2026 1verdicts
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Sets with Few Subset Sums
Stability versions of the inverse theorem for subset sums are proved: n-element positive real sets with at most binom(n+1,2)+1+M subset sums are characterized for M up to n-4, and sets with O(n^2) subset sums are characterized up to constants.