{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T23:34:23Z","timestamp":1773444863584,"version":"3.50.1"},"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>Graham, R\u00f6dl, and Ruci\u0144ski originally posed the problem of determining the minimum number of monochromatic Schur triples that must appear in any 2-coloring of the first n integers. This question was subsequently resolved independently by Datskovsky, Schoen, and Robertson and Zeilberger. Here we suggest studying a natural anti-Ramsey variant of this question and establish the first non-trivial bounds by proving that the maximum fraction of Schur triples that can be rainbow in a given 3-coloring of the first n integers is at least 0.4 and at most 0.66364. We conjecture the lower bound to be tight. This question is also motivated by a famous analogous problem in graph theory due to Erd\u0151s and S\u00f3s regarding the maximum number of rainbow triangles in any 3-coloring of Kn, which was settled by Balogh et al..<\/jats:p>","DOI":"10.37236\/13554","type":"journal-article","created":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:22:09Z","timestamp":1773440529000},"source":"Crossref","is-referenced-by-count":0,"title":["An Unsure Note on an Un-Schur Problem"],"prefix":"10.37236","volume":"33","author":[{"given":"Olaf","family":"Parczyk","sequence":"first","affiliation":[]},{"given":"Christoph","family":"Spiegel","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p45\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:22:16Z","timestamp":1773440536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/13554","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,13]]},"article-number":"P1.45"}}