{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T18:51:24Z","timestamp":1769971884004,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove several expanders with exponent strictly greater than $2$. For any finite set $A \\subset \\mathbb R$, we prove the following six-variable expander results:$|(A-A)(A-A)(A-A)| \\gg \\frac{|A|^{2+\\frac{1}{8}}}{\\log^{\\frac{17}{16}}|A|},$$\\left|\\frac{A+A}{A+A}+\\frac{A}{A}\\right| \\gg \\frac{|A|^{2+\\frac{2}{17}}}{\\log^{\\frac{16}{17}}|A|},$\u00a0$\\left|\\frac{AA+AA}{A+A}\\right| \\gg \\frac{|A|^{2+\\frac{1}{8}}}{\\log |A|},$\u00a0$\\left|\\frac{AA+A}{AA+A}\\right| \\gg \\frac{|A|^{2+\\frac{1}{8}}}{\\log |A|}.$<\/jats:p>","DOI":"10.37236\/7050","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:50:38Z","timestamp":1578653438000},"source":"Crossref","is-referenced-by-count":9,"title":["Expanders with Superquadratic Growth"],"prefix":"10.37236","volume":"24","author":[{"given":"Antal","family":"Balog","sequence":"first","affiliation":[]},{"given":"Oliver","family":"Roche-Newton","sequence":"additional","affiliation":[]},{"given":"Dmitry","family":"Zhelezov","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p14\/pdf_1","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p14\/pdf_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:50:35Z","timestamp":1579218635000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,28]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/7050","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,28]]},"article-number":"P3.14"}}