{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:16Z","timestamp":1753893856208,"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>We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of $\\{1,...,n\\}$ containing  no solutions to a wide class of non-invariant, homogeneous linear equations in three variables, i.e.: equations of the form $ax+by=cz$ with  $a+b \\neq c$.<\/jats:p>","DOI":"10.37236\/992","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:47:57Z","timestamp":1578718077000},"source":"Crossref","is-referenced-by-count":2,"title":["Extremal Subsets of $\\{1,...,n\\}$ Avoiding Solutions to Linear Equations in Three Variables"],"prefix":"10.37236","volume":"14","author":[{"given":"Peter","family":"Hegarty","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,11,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r74\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:59:46Z","timestamp":1579319986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/992","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,11,5]]},"article-number":"R74"}}