{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T11:44:52Z","timestamp":1648986292820},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"A planar point-set $X$ in Euclidean plane is called a $k$-distance set if there are exactly $k$ different distances among the points in $X$. The function $g(k)$ denotes the maximum number of points in the Euclidean plane that is a $k$-distance set. In 1996,\u00a0Erd\u0151s and Fishburn conjectured that for $k\\geq 7$, every $g(k)$-point subset of the plane that determines $k$ different distances is similar to a subset of the triangular lattice. We believe that if $g(k)$ is an increasing function of $k$, then the conjecture is false. We present data that supports our claim and a method of construction that unifies known optimal point configurations for $k\\geq 3$.<\/jats:p>","DOI":"10.37236\/3263","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:11:29Z","timestamp":1578705089000},"source":"Crossref","is-referenced-by-count":0,"title":["Sparse Distance Sets in the Triangular Lattice"],"prefix":"10.37236","volume":"20","author":[{"given":"Tanbir","family":"Ahmed","sequence":"first","affiliation":[]},{"given":"Hunter","family":"Snevily","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,12,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:10:27Z","timestamp":1579259427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3263","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,17]]}}}