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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the size of finite Sidon sequences

Author: Sheng Chen
Journal: Proc. Amer. Math. Soc. 121 (1994), 353-356
MSC: Primary 11B83; Secondary 11B50
MathSciNet review: 1196162
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Abstract: Let $ h \geq 2$ be an integer. A set of positive integers B is called a $ {B_h}$-sequence, or a Sidon sequence of order h, if all sums $ {a_1} + {a_2} + \cdots + {a_h}$, where $ {a_i} \in B (i = 1,2, \ldots ,h)$, are distinct up to rearrangements of the summands. Let $ {F_h}(n)$ be the size of the maximum $ {B_h}$-sequence contained in $ \{ 1,2, \ldots ,n\} $. We prove that

$\displaystyle {F_{2r - 1}}(n) \leq {({(r!)^2}n)^{1/(2r - 1)}} + O({n^{1/(4r - 2)}}).$

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Additional Information

PII: S 0002-9939(1994)1196162-9
Keywords: Additive number theory, difference sets, $ {B_h}$-sequence, Sidon sequences
Article copyright: © Copyright 1994 American Mathematical Society

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