Difference Sets of Null Density Subsets of N

DOI: 10.4236/apm.2012.23027   PDF   HTML     4,525 Downloads   7,640 Views   Citations

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 .

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D. Dastjerdi and M. Hosseini, "Difference Sets of Null Density Subsets of N," Advances in Pure Mathematics, Vol. 2 No. 3, 2012, pp. 195-199. doi: 10.4236/apm.2012.23027.

Conflicts of Interest

The authors declare no conflicts of interest.

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