## DIMACS TR: 94-01

## Inverse Theorems for Subset Sums

### Author: Melvyn B. Nathanson

**
ABSTRACT
**

Let $A$ be a finite set of integers. For $h \geq 1$,
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 determine
the structure of the finite 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.

Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1994/94-01.ps

DIMACS Home Page