{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:31Z","timestamp":1753893811992,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Using recent developments on the theory of locally decodable codes, we prove that the critical size for Szemer\u00e9di's theorem with random differences is bounded from above by $N^{1-\\frac{2}{k} + o(1)}$ for length-$k$ progressions. This improves the previous best bounds of $N^{1-\\frac{1}{\\lceil k\/2 \\rceil} + o(1)}$ for all odd $k$.<\/jats:p>","DOI":"10.37236\/12415","type":"journal-article","created":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T15:45:29Z","timestamp":1727970329000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Threshold for Szemer\u00e9di's Theorem with Random Differences"],"prefix":"10.37236","volume":"31","author":[{"given":"Jop","family":"Bri\u00ebt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davi","family":"Castro-Silva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,10,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T15:45:29Z","timestamp":1727970329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,4]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12415","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,10,4]]},"article-number":"P4.8"}}