{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:29:07Z","timestamp":1773145747918,"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>Let $D(n)$ denote the cardinality of the largest subset of the set $\\{1,2,\\ldots,n\\}$ such that the difference of no pair of distinct elements is a square. A well-known theorem of Furstenberg and S\u00e1rk\u00f6zy states that $D(n)=o(n)$. In the other direction, Ruzsa has proven that $D(n) \\gtrsim n^{\\gamma}$ for $\\gamma = \\frac{1}{2}\\left( 1 + \\frac{\\log 7}{\\log 65} \\right) \\approx 0.733077$. We improve this to $\\gamma = \\frac{1}{2}\\left( 1 + \\frac{\\log 12}{\\log 205} \\right) \u00a0\\approx 0.733412$.<\/jats:p>","DOI":"10.37236\/4656","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:31:52Z","timestamp":1578702712000},"source":"Crossref","is-referenced-by-count":3,"title":["An improved lower bound related to the Furstenberg-S\u00e1rk\u00f6zy theorem"],"prefix":"10.37236","volume":"22","author":[{"given":"Mark","family":"Lewko","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,2,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:37:06Z","timestamp":1579257426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4656","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,16]]},"article-number":"P1.32"}}