If A is a finite set of positive integers, let Eh, (A) denote the set of h-fold sums and h-fold products of elements of A. This paper is concerned with the behavior of the function fh(k), the minimum of |Eh,(A)| taken over all A with |A| = k. Upper and lower bounds for fh, (k) are proved, improving bounds given by Erdos, Szemerédi, and Nathanson. Moreover, the lower bound holds when we allow A to be a finite set of arbitrary positive real numbers.
|Original language||English (US)|
|Number of pages||8|
|State||Published - Dec 1 1998|
ASJC Scopus subject areas
- Algebra and Number Theory