Inverse theorems for subset sums

Author:
Melvyn B. Nathanson

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1409-1418

MSC:
Primary 11B13; Secondary 11B25, 11B75

DOI:
https://doi.org/10.1090/S0002-9947-1995-1273512-1

MathSciNet review:
1273512

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite set of integers. For , let denote the set of all sums of distinct elements of . Let denote the set of all nonempty sums of distinct elements of . The direct problem for subset sums is to find lower bounds for and in terms of . The inverse problem for subset sums is to determine the structure of the extremal sets of integers for which and are minimal. In this paper both the direct and the inverse problem for subset sums are solved.

**[1]**G. A. Freiman,*On the addition of finite sets*. I, Izv. Vyssh. Uchebn. Zaved. Mat.**13**(1959), 202-213.**[2]**M. B. Nathanson,*The simplest inverse problems in additive number theory*, Number Theory with an Emphasis on the Markoff Spectrum (A. Pollington and W. Moran, eds.), Marcel Dekker, 1993, pp. 191-206.**[3]**-,*Additive number theory*:*Inverse theorems and the geometry of sumsets*, Springer-Verlag, New York, 1995.**[4]**A. Sárközy,*Finite addition theorems*. II, J. Number Theory**48**(1994), 197-218.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1273512-1

Keywords:
Additive number theory,
subset sums,
inverse theorems

Article copyright:
© Copyright 1995
American Mathematical Society