## DIMACS TR: 94-03

## Independence of Solution Sets and Minimal Asymptotic Bases

### Authors: Paul Erdos, Melvyn B. Nathanson and Prasad Tetali

**
ABSTRACT
**

Let $k \geq 2$. The set $A$ of nonnegative integers is a minimal
asymptotic basis of order $k$ if every sufficiently large integer
can be written as the sum of $k$ elements of $A$, but
no proper subset of $A$ has this property. In this paper,
combinatorial methods are used to find criteria for an asymptotic
basis of order $k$ to contain a minimal asymptotic basis of order $k$,
and probabilistic methods are used to prove the existence of
asymptotic bases that satisfy these criteria.

Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1994/94-03.ps

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