Inverse theorems for subset sums
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 by Melvyn B. Nathanson PDF
 Trans. Amer. Math. Soc. 347 (1995), 14091418 Request permission
Abstract:
Let $A$ be a finite set of integers. For $h \geqslant 1$, let ${S_h}(A)$ denote the set of all sums of $h$ distinct elements of $A$. Let $S(A)$ denote the set of all nonempty sums of distinct elements of $A$. The direct problem for subset sums is to find lower bounds for ${S_h}(A)$ and $S(A)$ in terms of $A$. The inverse problem for subset sums is to determine the structure of the extremal sets $A$ of integers for which ${S_h}(A)$ and $S(A)$ are minimal. In this paper both the direct and the inverse problem for subset sums are solved.References

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—, Additive number theory: $2$ Inverse theorems and the geometry of sumsets, SpringerVerlag, New York, 1995.
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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 347 (1995), 14091418
 MSC: Primary 11B13; Secondary 11B25, 11B75
 DOI: https://doi.org/10.1090/S00029947199512735121
 MathSciNet review: 1273512