On sums of dilates

  • Authors:

  • Javier Cilleruelo;Yahya o. Hamidoune;Oriol Serra

  • Affiliations:

  • 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 ...;Upmc université paris 06, e. combinatoire, case 189, 4 place jussieu, 75005 paris, france (e-mail: hamidoune@math.jussieu.fr);Universitat politécnica de catalunya, jordi girona, 1, e-08034 barcelona, spain (e-mail: oserra@ma4.upc.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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.