{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:18:12Z","timestamp":1759335492978,"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>We show an improved upper estimate for van der Waerden number $W(3,k):$ there is an absolute constant $c&gt;0$ such that if $\\{1,\\dots,N\\}=X\\cup Y$ is a partition such that $X$ does not contain any arithmetic progression of length $3$ and $Y$ does not contain any arithmetic progression of length $k$ then\r\n$$N\\le \\exp(O(k^{1-c}))\\,.$$<\/jats:p>","DOI":"10.37236\/9704","type":"journal-article","created":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T09:20:44Z","timestamp":1623144044000},"source":"Crossref","is-referenced-by-count":2,"title":["A Subexponential Upper Bound for van der Waerden Numbers $W(3,k)$"],"prefix":"10.37236","volume":"28","author":[{"given":"Tomasz","family":"Schoen","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,6,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T09:20:45Z","timestamp":1623144045000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i2p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,4]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9704","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,6,4]]},"article-number":"P2.34"}}