Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11B83, 11B50

Retrieve articles in all journals with MSC: 11B83, 11B50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1196162-9
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