On the Combinatorics of Projective Mappings
György Elekes
and Zoltán Király
DOI: 10.1023/A:1012799318591
Abstract
We consider composition sets of one-dimensional projective mappings and prove that small composition sets are closely related to Abelian subgroups.
Pages: 183–197
Keywords: projective mapping; composition set; abelian subgroup
Full Text: PDF
References
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2. J. Beck, “On the lattice property of the plane and some problems of Dirac, Motzkin and Erd\Acute\Acute os,” Combinatorica 3 (3-4) (1983), 281-297.
3. Y. Bilu, “Structure of sets with small sumset,” Asterisque, SMF 258 (1999), 77-108.
4. G. Elekes, “On linear combinatorics I,” Combinatorica 17 (4) (1997), 447-458.
5. G. Elekes, “On linear combinatorics II,” Combinatorica 18 (1) (1998), 13-25.
6. G. A. Freiman, Foundations of a Structural Theory of Set Addition, Translation of Mathematical Monographs vol.
37. Amer. Math. Soc., Providence, R.I., USA, 1973.
7. R. Graham and J. Ne\check set\check ril (Eds.), The Mathematics of Paul Erd\Acute\Acute os, Springer-Verlag, Berlin, 1996.
8. M. Laczkovich and I.Z. Ruzsa, “The number of homothetic subsets,” in The Mathematics of Paul Erdos, R. Graam and J. Ne\check set\check ril(Eds.), Springer-Verlag, Berlin, 1996.
9. J. Pach and P. K. Agarwal, Combinatorial Geometry, J. Wiley and Sons, New York, 1995.
10. J. Pach and M. Sharir, “On the number of incidences between points and curves,” Combinatorics, Probability and Computing 7 (1998), 121-127.
11. I. Z. Ruzsa, “Arithmetical progressions and the number of sums,” Periodica Math. Hung. 25 (1992), 105-111.
12. I. Z. Ruzsa, “Generalized arithmetic progressions and sum sets,” Acta Math. Sci. Hung. 65 (1994), 379-388.