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 .