{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:07:47Z","timestamp":1758823667202,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>If $k$ is a positive integer, we say that a set $A$ of positive integers is $k$-sum-free if there do not exist $a,b,c$ in $A$ such that $a + b = kc$. In particular we give a precise characterization of the structure of maximum sized $k$-sum-free sets in $\\{1,\\ldots,n\\}$ for $k\\ge 4$ and $n$ large.<\/jats:p>","DOI":"10.37236\/1916","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:18:04Z","timestamp":1578719884000},"source":"Crossref","is-referenced-by-count":6,"title":["The Structure of Maximum Subsets of $\\{1,\\ldots,n\\}$ with No Solutions to $a+b = kc$"],"prefix":"10.37236","volume":"12","author":[{"given":"Andreas","family":"Baltz","sequence":"first","affiliation":[]},{"given":"Peter","family":"Hegarty","sequence":"additional","affiliation":[]},{"given":"Jonas","family":"Knape","sequence":"additional","affiliation":[]},{"given":"Urban","family":"Larsson","sequence":"additional","affiliation":[]},{"given":"Tomasz","family":"Schoen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,4,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:50:03Z","timestamp":1579323003000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,4,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1916","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,4,28]]},"article-number":"R19"}}