{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:20Z","timestamp":1753893860426,"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>Every set of points $\\mathcal{P}$ determines $\\Omega(|\\mathcal{P}| \/ \\log |\\mathcal{P}|)$ distances. A close version of this was initially conjectured by Erd\u0151s in 1946 and rather recently proved by Guth and Katz. We show that when near this lower bound, a point set $\\mathcal{P}$ of the form $A \\times A$ must satisfy $|A - A| \\ll |A|^{2-\\frac{2}{7}} \\log^{\\frac{1}{7}} |A|$. This improves recent results of Hanson and Roche-Newton.\u00a0\r\n<\/jats:p>","DOI":"10.37236\/7736","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:10:12Z","timestamp":1578640212000},"source":"Crossref","is-referenced-by-count":1,"title":["On Cartesian Products which Determine Few Distinct Distances"],"prefix":"10.37236","volume":"26","author":[{"given":"Cosmin","family":"Pohoata","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,1,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p7\/7766","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p7\/7766","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:19:08Z","timestamp":1579234748000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7736","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,1,11]]},"article-number":"P1.7"}}