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Sidon Sets

Published online by Cambridge University Press:  20 November 2018

H. L. Abbott
H. L. Abbott*
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta, Canada T6G 2G1
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Abstract

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Denote by g(n) the largest integer m such that every set of integers of size n contains a subset of size m whose pairwise sums are distinct. It is shown that g(n) > cn1/2 for any constant c < 2/25 and all sufficiently large n.

Keywords

11B75

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 335 - 341
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Ajtai, M., Komlös, J., Szemerédi, E., A dense infinite Sidon sequence, European Journal of Combinatorics, 2 (1981), 1–11.Google Scholar
2. Bose, R. C., An affine analogue of Singer's Theorem, Journal of the Indian Math. Soc, 6 (1942), 1–15.Google Scholar
3. Bose, R. C. and Chowla, S., Theorems in the additive theory of numbers, Comment. Math. Helvet., 37 (1962-63), 141–147.Google Scholar
4. Chowla, S., Solution of a problem of Erdös and Turán in additive number theory, Proc. Nat. Acad. Sci. India, 14 (1944), 1–2.Google Scholar
5. P. Erdös and Turän, P., On a problem of Sidon in additive number theory and some related problems, Jour. Lond. Math. Soc, 16 (1941), 212–215. addendum, ibid. 19 (1944), 208.Google Scholar
6. Halberstam, H. and Roth, K. F., Sequences, Oxford University Press, 1966.Google Scholar
7. Komlös, J., Sulyok, M. and Szemerédi, E., Linear problems in combinatorial number theory, Acta Math. Acad. Sci. Hung., 26 (1975), 113–121.Google Scholar
8. Mian, A. and S. Chowla, On the B2-squences of Sidon, Proc. Nat. Acad. Sci. India, 14 (1944), 3–4.Google Scholar
9. Sidon, S., Ein Satz uber trigonomietrische Polynöme und seine Anwendungen in der Théorie der Fourier-Reihen, Math. Ann., 106 (1932), 536–539.Google Scholar
10. Sidon, S., Uber die Fourier Konstanten der Funktionen der Klasse Lp für p > 1, Acta Sci. Math. Szeged, 7 (1935), 175–176.+1,+Acta+Sci.+Math.+Szeged,+7+(1935),+175–176.>Google Scholar
11. Singer, J., A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc, 43 (1938), 377–385.Google Scholar
12. Rudin, W., Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227.Google Scholar