Representation of elements of a sequence by sumsets


In this note the method of [5] and a result from [3] are combined to treat the following classical problem: Given a finite setA and an infinite sequenceS (both inZ), what is the minimal number of elements ofA whose sum lies inS? We obtain an upper bound depending only on the densities ofA andS (but not on their arithmetic nature).

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Lev, V.F. Representation of elements of a sequence by sumsets. Combinatorica 16, 587–590 (1996).

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Mathematics Subject Classification (1991)

  • 11 B 13
  • 11 B 75