Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Inverse theorems for subset sums


Author: Melvyn B. Nathanson
Journal: Trans. Amer. Math. Soc. 347 (1995), 1409-1418
MSC: Primary 11B13; Secondary 11B25, 11B75
MathSciNet review: 1273512
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $ \vert{S_h}(A)\vert$ and $ \vert S(A)\vert$ in terms of $ \vert A\vert$. The inverse problem for subset sums is to determine the structure of the extremal sets $ A$ of integers for which $ \vert{S_h}(A)\vert$ and $ \vert S(A)\vert$ are minimal. In this paper both the direct and the inverse problem for subset sums are solved.


References [Enhancements On Off] (What's this?)

  • [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: $ 2$ 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.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11B13, 11B25, 11B75

Retrieve articles in all journals with MSC: 11B13, 11B25, 11B75


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1273512-1
PII: S 0002-9947(1995)1273512-1
Keywords: Additive number theory, subset sums, inverse theorems
Article copyright: © Copyright 1995 American Mathematical Society