Corpus ID: 235435935

Highly sparse sets as additive complements for a prescribed density

  title={Highly sparse sets as additive complements for a prescribed density},
  author={H. Chu},
  • H. Chu
  • Published 2021
  • Mathematics
Given a set B ⊂ N, we investigate the existence of a set A ⊂ N such that the sumset A + B = {a + b : a ∈ A, b ∈ B} has a prescribed asymptotic density. A set B = {b1, b2, . . .} is said to be highly sparse if B is either finite or infinite with limj→∞ bj+1/bj = ∞. In this note, we prove that if B is highly sparse, such a set A exists. This generalizes a recent result by Faisant et al. 


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