{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852822,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $n$ and $k$ be integers. A set $A\\subset\\mathbb{Z}\/n\\mathbb{Z}$ is $k$-free if for all $x$ in $A$, $kx\\notin A$. We determine the maximal cardinality of such a set when $k$ and $n$ are coprime. We also study several particular cases and we propose an efficient algorithm for solving the general case. We finally give the asymptotic behaviour of the minimal size of a $k$-free set in $\\left[ 1,n\\right]$ which is maximal for inclusion.<\/jats:p>","DOI":"10.37236\/4704","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:06:06Z","timestamp":1578701166000},"source":"Crossref","is-referenced-by-count":0,"title":["On Modular $k$-Free Sets"],"prefix":"10.37236","volume":"22","author":[{"given":"Victor","family":"Lambert","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,4,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:17:32Z","timestamp":1579256252000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,29]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4704","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,4,29]]},"article-number":"P2.18"}}