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V. Bergelson and N. Hindman, “Additive and Multiplica- tive Ramsey Theorems in Some Elementary Results,” Combinatorics, Probability and Computing, Vol. 2, 1993, pp. 221-241. doi:10.1017/S0963548300000638

has been cited by the following article:

• TITLE: Difference Sets of Null Density Subsets of N

  AUTHORS: Dawoud Ahmadi Dastjerdi, Maryam Hosseini

  KEYWORDS: Difference Set; Density; -Set

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.3, May 29, 2012

  ABSTRACT: Let , and for any , . If is positive, then B is considered as a large set with . Its difference set has both high density and rich structure. The set with is also relatively large and it is a long standing conjecture that like sets with positive upper density they have arithmetic progression of arbitrary length. Here we show their difference set may not be substantial; for any there exists such that and .