{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:06Z","timestamp":1753893786906,"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>The $n$-th Heilbronn number, $H_n$, is the largest value such that $n$ points can be placed in the unit square in such a way that all possible triangles defined by any three of the points have area at least $H_n$. In this note we establish new bounds for the first Heilbronn numbers. These new values have been found by using a simple implementation of simulated annealing to obtain a first approximation and then optimizing the results by finding the nearest exact local maximum.<\/jats:p>","DOI":"10.37236\/1623","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:27:27Z","timestamp":1578709647000},"source":"Crossref","is-referenced-by-count":3,"title":["New Lower Bounds for Heilbronn Numbers"],"prefix":"10.37236","volume":"9","author":[{"given":"Francesc","family":"Comellas","sequence":"first","affiliation":[]},{"given":"J. Luis A.","family":"Yebra","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2002,2,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:16:05Z","timestamp":1579324565000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1623","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,2,2]]},"article-number":"R6"}}