Difference Sets of Null Density Subsets of N - Advances in Pure Mathematics

APM > Vol.2 No.3, May 2012

Advances in Pure Mathematics

Volume 2, Issue 3 (May 2012)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

Google-based Impact Factor: 0.50 Citations h5-index & Ranking

Difference Sets of Null Density Subsets of N ()

HTML

Download as PDF (Size: 147KB) PP. 195-199

DOI: 10.4236/apm.2012.23027 4,817 Downloads 8,261 Views Citations

Author(s)

Dawoud Ahmadi Dastjerdi, Maryam Hosseini

Affiliation(s)

Department of Mathematics, University of Guilan, Rasht, Iran.

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 .

KEYWORDS

Difference Set; Density; -Set

Share and Cite:

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.

Cited by