Generalized arithmetical progressions and sumsets

@article{Ruzsa1994GeneralizedAP,
  title={Generalized arithmetical progressions and sumsets},
  author={Imre Z. Ruzsa},
  journal={Acta Mathematica Hungarica},
  year={1994},
  volume={65},
  pages={379-388}
}
  • I. Ruzsa
  • Published 1 December 1994
  • Mathematics
  • Acta Mathematica Hungarica
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References

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I . Let K = {ao,al . . . . . ak_l } be a f i n i t e set of in teger vectors , l e t 2K = K + K = {~ E~m : # = ai + a j l a i ' a j E K} be i t s sum set , and l e t T = 12K I be the c a r d i n a l
A Tribute to Paul Erdős: On arithmetic progressions in sums of sets of integers
3 Proof of Theorem 1 9 3.1 Estimation of the g1 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Estimation of the g3 term. . . . . . . . . . . . . . . . . . . . . . . .
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the Schnirelmann and lower asymptotic densities respectively of d. According to Schnirelmann theory (see [9]), if 1 > as/ > 0 and Oes/ then a(2s/) ^ 2a(s/)-a(s/) > a(s/); and if a(s/)^\ then 2s/ =