On the structure of sets with small doubling property on the plane (I)

• Autorzy: Yonutz Stanchescu
• Języki publikacji: EN

Abstrakty

EN

Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.

Kategorie tematyczne

• 11B99: None of the above, but in this section
• 11P99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 83
• Numer: 2
• Strony: 127-141

Daty

wydano

1998

otrzymano

1996-12-20

poprawiono

1997-05-20

Twórcy

autor

Yonutz Stanchescu

• School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel

Bibliografia

• [B] Y. Bilu, Structure of sets with small sumsets, Mathématiques Stochastiques, Univ. Bordeaux 2, Preprint 94-10, Bordeaux, 1994.
• [F1] G. A. Freiman, Foundations of a Structural Theory of Set Addition, Transl. Math. Monographs 37, Amer. Math. Soc., Providence, R.I., 1973.
• [F2] G. A. Freiman, Inverse problems in additive number theory VI. On the addition of finite sets III, Izv. Vyssh. Uchebn. Zaved. Mat. 1962, no. 3 (28), 151-157 (in Russian).
• [F3] G. A. Freiman, What is the structure of K if K + K is small?, in: Lecture Notes in Math. 1240, Springer, 1987, New York, 109-134.
• [L-S] V. F. Lev and P. Y. Smeliansky, On addition of two distinct sets of integers, Acta Arith. 70 (1995), 85-91.
• [R] I. Z. Ruzsa, Generalized arithmetical progressions and sumsets, Acta Math. Hungar. 65 (1994), 379-388.
• [S] Y. Stanchescu, On addition of two distinct sets of integers, Acta Arith. 75 (1996), 191-194.