Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T00:28:58.033Z Has data issue: false hasContentIssue false
  • English
  • Français

On Sums of Dilates

Published online by Cambridge University Press:  09 July 2009

JAVIER CILLERUELO ,
YAHYA O. HAMIDOUNE  and
ORIOL SERRA
JAVIER CILLERUELO
Affiliation:
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) and Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049-Madrid, Spain (e-mail: franciscojavier.cilleruelo@uam.es)
YAHYA O. HAMIDOUNE
Affiliation:
UPMC Université Paris 06, E. Combinatoire, Case 189, 4 Place Jussieu, 75005 Paris, France (e-mail: hamidoune@math.jussieu.fr)
ORIOL SERRA
Affiliation:
Universitat Politécnica de Catalunya, Jordi Girona, 1, E-08034 Barcelona, Spain (e-mail: oserra@ma4.upc.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

For k prime and A a finite set of integers with |A| ≥ 3(k − 1)2(k − 1)! we prove that |A + k · A| ≥ (k + 1)|A| − ⌈k(k + 2)/4⌉ where k · A = {ka: a ∈ A}. We also describe the sets for which equality holds.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 6 , November 2009 , pp. 871 - 880
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bukh, B. (2008) Sums of dilates. Combin. Probab. Comput. 17 627–639.Google Scholar
[2]Cilleruelo, J., Silva, M. and Vinuesa, C. A sumset problem. Preprint.Google Scholar
[3]Nathanson, M. B. Inverse problems for linear forms over finite sets of integers. Available from: arXiv:0708.2304.Google Scholar