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The Maximal Density of Product-Free Sets in Z/nZ
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2013 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 4, 827-845 p.Article in journal (Refereed) Published
Abstract [en]

This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which there is no solution to ab=c (mod n), with a, b, c being in the set. In a previous paper, we constructed an infinite sequence of integers (n(i))(i >= 1) and product-free sets S-i in Z/n(i)Z such that the density vertical bar S-i vertical bar/n(i) -> 1 as i -> infinity, where vertical bar S-i vertical bar denotes the cardinality of S-i. Here, we obtain matching, up to constants, upper and lower bounds on the maximal attainable density as n -> infinity.

Place, publisher, year, edition, pages
2013. no 4, 827-845 p.
Keyword [en]
Sum-Free Sets
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-119485DOI: 10.1093/imrn/rns014ISI: 000315152800003Scopus ID: 2-s2.0-84874353080OAI: oai:DiVA.org:kth-119485DiVA: diva2:611214
Funder
Swedish Research Council
Note

QC 20130315

Available from: 2013-03-15 Created: 2013-03-14 Last updated: 2017-12-06Bibliographically approved

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Kurlberg, Pär

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