{"paper":{"title":"On constant-multiple-free sets contained in a random set of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Sang June Lee","submitted_at":"2012-12-20T14:46:29Z","abstract_excerpt":"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 $rx = y$.\n  The extremal problem on estimating the maximum possible size of $r$-multiple-free sets contained in $[n]:={1,2,...,n}$ has been studied for its own interest in combinatorial number theory and application to coding theory. Let $a$, $b$ be positive integers such that $a<b$ and the greatest common divisor of $a$ and $b$ is 1. Wakeham and Wood showed that the maximum size of $(b/a)$-multiple-free sets contained in $[n]$ is $\\frac{b}{b+1}n+O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5063","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}