$[n]:={1,2,cdots,n}$ 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
In this note we generalize this result as follows. For a real number $pin (0,1)$, let $[n]_p$ be a set of integers obtained by choosing each element $iin [n]$ randomly and independently with probability $p$. We
show that the maximum possible size of $(b/a)$-multiple-free sets contained in $[n]_p$ is $frac{b}{b+p}pn+O(sqrt{pn}log n log log n)$ with probability that goes to $1$ as $n o infty$.
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1371011138_0.877124.pdf