DC Field | Value | Language |
---|---|---|
dc.contributor.author | Lee, Sang June | ko |
dc.date.accessioned | 2014-08-29T01:29:34Z | - |
dc.date.available | 2014-08-29T01:29:34Z | - |
dc.date.created | 2014-02-17 | - |
dc.date.created | 2014-02-17 | - |
dc.date.issued | 2014-01 | - |
dc.identifier.citation | ARS COMBINATORIA, v.113A, pp.247 - 256 | - |
dc.identifier.issn | 0381-7032 | - |
dc.identifier.uri | http://hdl.handle.net/10203/188762 | - |
dc.description.abstract | For a rational number r > 1, a set A of positive integers is called an r-multiple-free set if A does not contain any solution of the equation rx = y. The extremal problem of estimating the maximum possible size of r-multiple-free sets contained in [n] := {1, 2, ... , n} has been studied in combinatorial number theory for theoretical interest and its application to coding theory. Let a and b be relatively prime positive integers such that a < b. Wakeham and Wood showed that the maximum size of (b/a)-multiple-free sets contained in [n] is b/b+1 n + O(log n). In this note we generalize this result as follows. For a real number p is an element of (0, 1), let [n](p) be a set of integers obtained by choosing each element i is an element of [n] randomly and independently with probability p. We show that the maximum possible size of (b/a)-multiple-free sets contained in [n](p) is b/b+p pn + O(root pn log n log log n) with probability that goes to 1 as n -> infinity. | - |
dc.language | English | - |
dc.publisher | CHARLES BABBAGE RES CTR | - |
dc.title | On constant-multiple-free sets contained in random sets of integers | - |
dc.type | Article | - |
dc.identifier.wosid | 000329883700021 | - |
dc.identifier.scopusid | 2-s2.0-84901988111 | - |
dc.type.rims | ART | - |
dc.citation.volume | 113A | - |
dc.citation.beginningpage | 247 | - |
dc.citation.endingpage | 256 | - |
dc.citation.publicationname | ARS COMBINATORIA | - |
dc.embargo.liftdate | 9999-12-31 | - |
dc.embargo.terms | 9999-12-31 | - |
dc.type.journalArticle | Article | - |
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