{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:05Z","timestamp":1753893845551,"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>Let $\\mathcal{P}$ be a set of $n$ points in the finite plane $\\mathbb{F}_q^2$ over the finite field $\\mathbb{F}_q$ of $q$ elements, where $q$ is an odd prime power. For any $s \\in \\mathbb{F}_q$, denote by $A (\\mathcal{P}; s)$ the number of ordered triangles whose vertices in $\\mathcal{P}$ having area $s$.  We show that if the cardinality of $\\mathcal{P}$ is large enough then $A (\\mathcal{P}; s)$ is close to the expected number $|\\mathcal{P}|^3\/q$.<\/jats:p>","DOI":"10.37236\/700","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:39:55Z","timestamp":1578713995000},"source":"Crossref","is-referenced-by-count":0,"title":["Distinct Triangle Areas in a Planar Point Set over Finite Fields"],"prefix":"10.37236","volume":"18","author":[{"given":"Le Anh","family":"Vinh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,10,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p213\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p213\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:00:19Z","timestamp":1579302019000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p213"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/700","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,31]]},"article-number":"P213"}}