Representation of elements of a sequence by sumsets

Abstract

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).

This is a preview of subscription content, access via your institution.

References

  1. [1]

    N. Alon: Subset Sums,J. Number Theory,27 (1987), 196–205.

    Google Scholar 

  2. [2]

    G. Freiman: Sumsets and powers of 2,Colloq. Math. Soc. János Bolyai 60 (1992), North-Holland, Amsterdam.

    Google Scholar 

  3. [3]

    V. Lev: Structure theorem for multiple set addition and the Frobenius problem,J. Number Theory,58 (1) (1996), 79–88.

    Google Scholar 

  4. [4]

    V. Lev: Optimal represenations by sumsets and subset sums,J. Number Theory, to appear.

  5. [5]

    V. Lev: Representing powers of 2 by a sum of four integers,Combinatorica,16(2) (1996), 1–4.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lev, V.F. Representation of elements of a sequence by sumsets. Combinatorica 16, 587–590 (1996). https://doi.org/10.1007/BF01271276

Download citation

Mathematics Subject Classification (1991)

  • 11 B 13
  • 11 B 75