{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:52Z","timestamp":1753893832868,"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>The solution to the problem of finding the minimum number of monochromatic triples $(x,y,x+ay)$ with $a\\geq 2$ being a fixed positive integer over any 2-coloring of $[1,n]$ was conjectured by Butler, Costello, and Graham (2010) and Thanathipanonda (2009). We solve this problem using a method based on Datskovsky's proof (2003) on the minimum number of monochromatic Schur triples $(x,y,x+y)$. We do this by exploiting the combinatorial nature of the original proof and adapting it to the general problem.<\/jats:p>","DOI":"10.37236\/6490","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:55:28Z","timestamp":1578671728000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Minimum Number of Monochromatic Generalized Schur Triples"],"prefix":"10.37236","volume":"24","author":[{"given":"Thotsaporn","family":"Thanatipanonda","sequence":"first","affiliation":[]},{"given":"Elaine","family":"Wong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,5,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:57:14Z","timestamp":1579237034000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6490","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,5,5]]},"article-number":"P2.20"}}