{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:05Z","timestamp":1753893785043,"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>This paper explores the relationship between convexity and sum sets. In particular, we show that elementary number theoretical methods, principally the application of a squeezing principle, can be augmented with the Elekes-Szab\u00f3 Theorem in order to give new information. Namely, if we let $A \\subset \\mathbb R$, we prove that there exist $a,a' \\in A$ such that\\[\\left | \\frac{(aA+1)^{(2)}(a'A+1)^{(2)}}{(aA+1)^{(2)}(a'A+1)} \\right | \\gtrsim |A|^{31\/12}.\\]We are also able to prove that\\[\\max \\{|A+ A-A|, |A^2+A^2-A^2|, |A^3 + A^3 - A^3|\\} \\gtrsim |A|^{19\/12}.\\]Both of these bounds are improvements of recent results and takes advantage of computer algebra to tackle some of the computations.<\/jats:p>","DOI":"10.37236\/11331","type":"journal-article","created":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T09:53:08Z","timestamp":1706262788000},"source":"Crossref","is-referenced-by-count":1,"title":["Convexity, Squeezing, and the Elekes-Szab\u00f3 Theorem"],"prefix":"10.37236","volume":"31","author":[{"given":"Oliver","family":"Roche-Newton","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elaine","family":"Wong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,1,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T09:53:08Z","timestamp":1706262788000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i1p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/11331","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,1,12]]},"article-number":"P1.3"}}