# New Upper Bounds for Finite Bh Sequences

```@article{Cilleruelo2001NewUB,
title={New Upper Bounds for Finite Bh Sequences},
author={Javier Cilleruelo},
year={2001},
volume={159},
pages={1-17}
}```
• J. Cilleruelo
• Published 15 April 2001
• Mathematics
Abstract Let F h ( N ) be the maximum number of elements that can be selected from the set {1, …,  N } such that all the sums a 1 +…+ a h , a 1 ⩽…⩽ a h are different. We introduce new combinatorial and analytic ideas to prove new upper bounds for F h ( N ). In particular we prove F 3 (N)⩽ 4 1+16/( π +2) 4 N 1/3 +o(N 1/3 ), F 4 (N)⩽ 8 1+16/( π +2) 4 N 1/4 +o(N 1/4 ). Besides, our techniques have an independent interest for further research in additive number theory.
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