{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815464,"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>In this paper we introduce a Ramsey type function $S(r;a,b,c)$ as the maximum $s$ such that for any $r$-coloring of ${\\Bbb N}$ there is a monochromatic sequence $x_1,x_2,\\ldots,x_s$ satisfying a homogeneous second order linear recurrence $ax_i+bx_{i+1}+cx_{i+2}=0$, $1\\leq i\\leq s-2$. We investigate $S(2;a,b,c)$ and evaluate its values for a wide class of triples $(a,b,c)$.<\/jats:p>","DOI":"10.37236\/310","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:16:17Z","timestamp":1578716177000},"source":"Crossref","is-referenced-by-count":1,"title":["On a Rado Type Problem for Homogeneous Second Order Linear Recurrences"],"prefix":"10.37236","volume":"17","author":[{"given":"Hayri","family":"Ardal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zden\u011bk","family":"Dvo\u0159\u00e1k","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Veselin","family":"Jungi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tom\u00e1\u0161","family":"Kaiser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2010,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:58:39Z","timestamp":1579305519000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/310","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,3,8]]},"article-number":"R38"}}