{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810144,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A\u00a0planar\u00a0point\u00a0set $X$ in\u00a0the Euclidean\u00a0plane\u00a0is\u00a0called\u00a0a\u00a0$k$-distance set\u00a0if\u00a0there\u00a0are\u00a0exactly\u00a0$k$ distances\u00a0between\u00a0two distinct\u00a0points\u00a0in $X$.\u00a0An\u00a0interesting\u00a0problem\u00a0is\u00a0to\u00a0find\u00a0the largest\u00a0possible\u00a0cardinality\u00a0of a $k$-distance\u00a0set.\u00a0This\u00a0problem was\u00a0introduced\u00a0by Erd\u0151s and\u00a0Fishburn (1996).\u00a0Maximum\u00a0planar sets\u00a0that\u00a0determine $k$ distances\u00a0for $k$ less than 5\u00a0have been\u00a0identi\ufb01ed.\u00a0The\u00a06-distance\u00a0conjecture\u00a0of\u00a0Erd\u0151s and Fishburn\u00a0states\u00a0that\u00a013\u00a0is the\u00a0maximum\u00a0number\u00a0of\u00a0points\u00a0in the plane that\u00a0determine\u00a0exactly\u00a06\u00a0different\u00a0distances. In\u00a0this paper,\u00a0we\u00a0prove the\u00a0conjecture.<\/jats:p>","DOI":"10.37236\/2917","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:10:14Z","timestamp":1578712214000},"source":"Crossref","is-referenced-by-count":2,"title":["A Proof of Erd\u0151s-Fishburn's Conjecture for $g(6)=13$"],"prefix":"10.37236","volume":"19","author":[{"given":"Wei","family":"Xianglin","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,12,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:22:24Z","timestamp":1579299744000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,6]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2917","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,12,6]]},"article-number":"P38"}}