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New Upper Bounds for Finite Bh Sequences

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Let Fh(N) be the maximum number of elements that can be selected from the set {1, …, N} such that all the sums a1+…+ah, a1…ah are different. We introduce new combinatorial and analytic ideas to prove new upper bounds for Fh(N). In particular we proveF3(N)41+16/(+2)4 N1/3+o(N1/3),F4( N)81+16/(+2)4 N1/4+o(N1/4).Besides, our techniques have an independent interest for further research in additive number theory. Copyright 2001 Academic Press.

Keywords: Bh sequences; Sidon sets

Document Type: Research Article

Affiliations: Departamento de Matematicas, Universidad Autónoma de Madrid, Madrid, 28049, Spain

Publication date: April 1, 2001

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