Alternative approach to sums of dilates

Rafał Bystrzycki and Tomasz Schoen
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 21—27
DOI: 10.7546/nntdm.2018.24.2.21-27
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Authors and affiliations

Rafał Bystrzycki
Department of Discrete Mathematics, Adam Mickiewicz University
ul. Umultowska 87, 61-614 Poznán, Poland

Tomasz Schoen
Department of Discrete Mathematics, Adam Mickiewicz University
ul. Umultowska 87, 61-614 Poznán, Poland

Abstract

We investigate the size of the sets λ1A + … + λhA, where λi are integers. Specifically, we look for upper bounds in terms of the doubling constant K = |A + A|/|A|. We also examine some situations in which those bounds can be significantly strengthened.

Keywords

  • Sumsets
  • Dilates
  • Ruzsa triangle inequality
  • Chang covering lemma

2010 Mathematics Subject Classification

  • 11P70

References

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  8. Tao, T.C. & Vu, H.V. (2006) Additive combinatorics, volume 105 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge.

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Cite this paper

APA

Bystrzycki, R. & Schoen, T. (2018). Alternative approach to sums of dilates. Notes on Number Theory and Discrete Mathematics, 24(2), 21-27, doi: 10.7546/nntdm.2018.24.2.21-27.

Chicago

Bystrzycki, R and Tomasz Schoen. “Alternative Approach to Sums of Dilates.” Notes on Number Theory and Discrete Mathematics 24, no. 2 (2018): 21-27, doi: 10.7546/nntdm.2018.24.2.21-27.

MLA

Bystrzycki, R and Tomasz Schoen. “Alternative Approach to Sums of Dilates.” Notes on Number Theory and Discrete Mathematics 24.2 (2018): 21-27. Print, doi: 10.7546/nntdm.2018.24.2.21-27.

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