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Sums of Dilates

Published online by Cambridge University Press:  01 September 2008

BORIS BUKH
BORIS BUKH*
Affiliation:
Department of Mathematics, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA (e-mail: [email protected])
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Abstract

The λ-dilate of a set A is λċA={λa : a∈A}. We give an asymptotically sharp lower bound on the size of sumsets of the form λ1ċA+ċċċ+λkċA for arbitrary integers λ1,. . .,λk and integer sets A. We also establish an upper bound for such sums, which is similar to, but often stronger than Plünnecke's inequality.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 5 , September 2008 , pp. 627 - 639
Copyright
Copyright © Cambridge University Press 2008

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