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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: bbukh@math.princeton.edu)
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Abstract

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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.

Information

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

References

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