Abstract
We show that ifp is prime andA is a sum-free subset of ℤ/ p ℤ withn:=|A|>0.33p, thenA is contained in a dilation of the interval [n,p−n] (modp).
Similar content being viewed by others
References
[DT89] A. Davydov and L. Tombak,Quasi-perfect linear binary codes with distance 4 and complete caps in projective geometry, Problemy Peredachi Informatzii25(4) (1989), 11–23.
[DFST99] J.-M. Deshouillers, G. Freiman, V. Sós and M. Temkin,On the structure of sum-free sets. II, Astérisque258 (1999), xii, 149–161.
[DY69] P. H. Diananda and H. P. Yap,Maximal sum-free sets of elements in finite groups, Proceedings of the Japan Academy45 (1969), 1–5.
[F62] G. A. Freiman,Inverse problems of additive number theory, VII. On addition of finite sets, IV, Izvestiya Vysshikh Uchebnykh Zavedeniy Matematika6(31) (1962), 131–144.
[F92] G. A. Freiman,On the structure and the number of sum-free sets, Astérisque209 (1992), 13, 195–201.
[G04] B. Green,The Cameron-Erdős Conjecture, The Bulletin of the London Mathematical Society36 (2004), 769–778.
[GR05] B. Green and I. Z. Ruzsa,Sum-free sets in abelian groups, Israel Journal of Mathematics147 (2005), 157–188.
[K98] K. S. Kedlaya,Product-free subsets of groups The American Mathematical Monthly105 (1998), 900–906.
[L03] V. F. Lev,Sharp estimates for the number of sum-free sets, Journal für die reine und angewandte Mathematik (Crelle's Journal)555 (2003), 1–25.
[L05] V. F. Lev,Large sum-free sets in ternary spaces, Journal of Combinatorial Theory, Series A111(2) (2005), 337–346.
[L] V. F. Lev,Distribution of points on arcs, INTEGERS, to appear.
[LS95] V. F. Lev and P. Y. Smeliansky,On addition of two distinct sets of integers, Acta Arithmetica70 (1995), 85–91.
[LLS01] T. Luczak, V. F. Lev and T. Schoen,Sum-free sets in abelian groups, Israel Journal of Mathematics125 (2001), 347–367.
[RS70] A. H. Rhemtulla and A. P. Street,Maximal sum-free sets in finite abelian groups, Bulletin of the Australian Mathematical Society2 (1970), 289–297.
[WSW72] J. S. Wallis, A. P. Street and W. D. Wallis,Combinatorics: Room squares, sum-free sets, Hadamard matrices Lecture Notes in Mathematics292, Springer-Verlag, Berlin, 1972.
[Y72] H. P. Yap,Maximal sum-free sets in finite abelian groups. IV, Nanta Mathematica5(3), (1972), 70–75.
[Y75] H. P. Yap,Maximal sum-free sets in finite abelian groups. V, Bulletin of the Australian Mathematical Society13 (1975), 337–342.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lev, V.F. Large sum-free sets in ℤ/ p ℤ. Isr. J. Math. 154, 221–233 (2006). https://doi.org/10.1007/BF02773607
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02773607