{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:28Z","timestamp":1753893868030,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A set in $\\mathbb R^d$ is called almost-equidistant\u00a0if for any three distinct points in the set, some two are at unit distance apart. First, we give a short proof of the result of Bezdek and L\u00e1ngi claiming that an almost-equidistant set lying on a $(d-1)$-dimensional sphere of radius $r$, where $r&lt;1\/\\sqrt{2}$, has at most $2d+2$ points. Second, we prove that an almost-equidistant set $V$ in $\\mathbb R^d$ has $O(d)$ points in two cases: if the diameter of $V$ is at most $1$ or if $V$ is a subset of a $d$-dimensional ball of radius at most $1\/\\sqrt{2}+cd^{-2\/3}$, where $c&lt;1\/2$. Also, we present a new proof of the result of Kupavskii, Mustafa and Swanepoel that an almost-equidistant set in $\\mathbb R^d$ has $O(d^{4\/3})$ elements.<\/jats:p>","DOI":"10.37236\/8044","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T02:07:59Z","timestamp":1578622079000},"source":"Crossref","is-referenced-by-count":0,"title":["On Almost-Equidistant Sets - II"],"prefix":"10.37236","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2423-6416","authenticated-orcid":false,"given":"Alexandr","family":"Polyanskii","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,5,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p14\/7827","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p14\/7827","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:14:41Z","timestamp":1579216481000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,3]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/8044","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,5,3]]},"article-number":"P2.14"}}