### Abstract

If A is a finite set of positive integers, let E_{h}, (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 f_{h}(k), the minimum of |E_{h},(A)| taken over all A with |A| = k. Upper and lower bounds for f_{h}, (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) |
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Pages (from-to) | 59-66 |

Number of pages | 8 |

Journal | Ramanujan Journal |

Volume | 2 |

Issue number | 1-2 |

State | Published - Dec 1 1998 |

Externally published | Yes |

### Keywords

- Products
- Sequences
- Sums

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Ford, K. (1998). Sums and products from a finite set of real numbers.

*Ramanujan Journal*,*2*(1-2), 59-66.