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On the size of finite Sidon sequences


Author: Sheng Chen
Journal: Proc. Amer. Math. Soc. 121 (1994), 353-356
MSC: Primary 11B83; Secondary 11B50
DOI: https://doi.org/10.1090/S0002-9939-1994-1196162-9
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

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


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

  • [1] R. C. Bose and S. Chowla, Theorems in the additive theory of numbers, Comment. Math. Helv. 37 (1962/1963), 141-147. MR 0144877 (26:2418)
  • [2] P. Erdős and P. Turan, On a problem in additive number theory and some related problems, J. Number Theory 38 (1941), 191-205.
  • [3] X.-D. Jia, On finite Sidon sequences, J. Number Theory 44 (1993), 84-92. MR 1219489 (94k:11014)
  • [4] M. A. Lee, On $ {B_3}$ sequences, Acta Math. Sinica 34 (1991), 67-71.
  • [5] B. Lindström, A remark on $ {B_4}$-sequences, J. Combin. Theory 7 (1969), 276-277. MR 0249389 (40:2634)
  • [6] S. Sidon, Ein Satz uber trigonomietrische Polynome und seine Anwendun gen in der Theorie der Fourier-Reihen, Math. Ann. 106 (1932), 536-539. MR 1512772

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1196162-9
Keywords: Additive number theory, difference sets, $ {B_h}$-sequence, Sidon sequences
Article copyright: © Copyright 1994 American Mathematical Society

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