{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:44Z","timestamp":1753893824712,"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>We give a construction of a non-degenerate polynomial $F\\in \\mathbb R[x,y,z]$ and a set $A$ of cardinality $n$ such that $F$ vanishes on $\\Omega(n^{3\/2})$ points of $A \\times A \\times A$, thus providing a new lower bound construction for the Elekes\u2013Szab\u00f3 problem.\u00a0We also give a related construction for the Elekes\u2013R\u00f3nyai problem restricted to a subgraph.\u00a0This consists of a polynomial $f\\in \\mathbb R[x,y]$ that is not additive or multiplicative, a set $A$ of size $n$,\u00a0and a subset $P\\subset A\\times A$ of size $\\Omega(n^{3\/2})$ on which $f$ takes only $n$ distinct values.<\/jats:p>","DOI":"10.37236\/8668","type":"journal-article","created":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:44:25Z","timestamp":1584578665000},"source":"Crossref","is-referenced-by-count":3,"title":["Constructions for the Elekes\u2013Szab\u00f3 and Elekes\u2013R\u00f3nyai problems"],"prefix":"10.37236","volume":"27","author":[{"given":"Mehdi","family":"Makhul","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"Roche-Newton","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Audie","family":"Warren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"De Zeeuw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,3,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p57\/8045","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p57\/8045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:44:25Z","timestamp":1584578665000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8668","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,3,20]]},"article-number":"P1.57"}}