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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

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

Abstract

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.

Bibliography

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Acta Arithmetica
1998/83/2
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Pages:
127-141
Main language of publication
English
Received
1996-12-20
Accepted
1997-05-20
Published
1998
Exact and natural sciences