{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833368,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The problem of finding the largest number of points in the unit cross-polytope\u00a0such that the $l_{1}$-distance between any two distinct points is\u00a0at least $2r$ is related to packings. For the $n$-dimensional cross-polytope, we show that $2n$ points\u00a0can be placed when $r\\in\\left(1-\\frac{1}{n},1\\right]$. For the three-dimensional\u00a0cross-polytope, $10$ and $12$ points can be placed if and only if\u00a0$r\\in\\left(\\frac{3}{5},\\frac{2}{3}\\right]$ and $r\\in\\left(\\frac{4}{7},\\frac{3}{5}\\right]$\u00a0respectively, and no more than $14$ points can be placed when $r\\in\\left(\\frac{1}{2},\\frac{4}{7}\\right]$.\u00a0Also, constructive arrangements of points that attain the upper bounds\u00a0of $2n$, $10$, and $12$ are provided, as well as $13$ points for\u00a0dimension $3$ when $r\\in\\left(\\frac{1}{2},\\frac{6}{11}\\right]$.<\/jats:p>","DOI":"10.37236\/8990","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:48Z","timestamp":1599187668000},"source":"Crossref","is-referenced-by-count":0,"title":["On Local Packings of the Cross-Polytope"],"prefix":"10.37236","volume":"27","author":[{"given":"Ji Hoon","family":"Chun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,8,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p38\/8156","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p38\/8156","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:48Z","timestamp":1599187668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,21]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8990","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,8,21]]},"article-number":"P3.38"}}