Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 826141, 11 pages
http://dx.doi.org/10.1155/2014/826141
Research Article

On the General Erdős-Turán Conjecture

1Université Jean Monnet, 23 rue Michelon, 42023 Saint-Étienne, France
2120 rue de Charonne, 75011 Paris, France
3Penn State University, 25 Yearsley Mill Road, Media, PA 19063, USA
4Kyläkunnantie 53, 00660 Helsinki, Finland

Received 28 July 2014; Accepted 14 October 2014; Published 17 November 2014

Academic Editor: Chris A. Rodger

Copyright © 2014 Georges Grekos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Erdős and P. Turán, “On a problem of Sidon in additive number theory,” Journal of the London Mathematical Society. Second Series, vol. 16, pp. 212–215, 1941. View at Google Scholar · View at MathSciNet
  2. H. Halberstam and K. F. Roth, Sequences, Clarendon Press, Oxford, UK, 1966. View at MathSciNet
  3. P. Erdős and W. H. Fuchs, “On a problem of additive number theory,” Journal of the London Mathematical Society, vol. 31, pp. 67–73, 1956. View at Google Scholar · View at MathSciNet
  4. G. Grekos, L. Haddad, C. Helou, and J. Pihko, “The class of Erdős-Turán sets,” Acta Arithmetica, vol. 117, no. 1, pp. 81–105, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. G. Grekos, L. Haddad, C. Helou, and J. Pihko, “On the Erdős-Turán conjecture,” Journal of Number Theory, vol. 102, no. 2, pp. 339–352, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. G. A. Dirac, “Note on a problem in additive number theory,” Journal of the London Mathematical Society, vol. 26, pp. 312–313, 1951. View at Google Scholar · View at MathSciNet
  7. M. Dowd, “Questions related to the Erdős-Turán conjecture,” SIAM Journal on Discrete Mathematics, vol. 1, no. 1, pp. 142–150, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. Helm, “Some remarks on the Erdős-Turán conjecture,” Acta Arithmetica, vol. 63, no. 4, pp. 373–378, 1993. View at Google Scholar · View at MathSciNet
  9. M. B. Nathanson, “Generalized additive bases, König's lemma, and the Erdős-Turán conjecture,” Journal of Number Theory, vol. 106, no. 1, pp. 70–78, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. L. Haddad and C. Helou, “Bases in some additive groups and the Erdős-Turán conjecture,” Journal of Combinatorial Theory Series A, vol. 108, no. 1, pp. 147–153, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Nešetřil and O. Serra, “The Erdős-Turán property for a class of bases,” Acta Arithmetica, vol. 115, no. 3, pp. 245–254, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. P. Borwein, S. Choi, and F. Chu, “An old conjecture of Erdős-Turán on additive bases,” Mathematics of Computation, vol. 75, no. 253, pp. 475–484, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. J. Nešetřil and O. Serra, “Semigroups with the Erdős-Turán property,” in Combinatorial Number Theory, pp. 381–388, de Gruyter, Berlin, Germany, 2007. View at Google Scholar
  14. Y.-G. Chen, “The analogue of Erdős-Turán conjecture in Zm,” Journal of Number Theory, vol. 128, no. 9, pp. 2573–2581, 2008. View at Google Scholar
  15. Y.-G. Chen, “On the Erdős-Turán conjecture,” Comptes Rendus de l'Académie des Sciences—Paris, vol. 350, pp. 933–935, 2012. View at Google Scholar
  16. Q.-H. Yang, “A generalization of Chen's theorem on the Erdős-Turán conjecture,” International Journal of Number Theory, vol. 9, no. 7, pp. 1683–1686, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus