{"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":1753893786986,"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>Let $s(N)$ denote the edge length of the smallest square in which one can pack $N$ unit squares. A duality method is introduced to prove that $s(6)=s(7)=3$. Let $n_r$ be the smallest integer $n$ such that $s(n^2+1)\\le n+{1\/r}$. We use an explicit construction to show that $n_r\\le 27r^3\/2+O(r^2)$, and also that $n_2\\le43$.<\/jats:p>","DOI":"10.37236\/1631","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:27:24Z","timestamp":1578691644000},"source":"Crossref","is-referenced-by-count":2,"title":["Efficient Packing of Unit Squares in a Square"],"prefix":"10.37236","volume":"9","author":[{"given":"Michael J","family":"Kearney","sequence":"first","affiliation":[]},{"given":"Peter","family":"Shiu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2002,2,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:16:02Z","timestamp":1579306562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1631","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,2,11]]},"article-number":"R14"}}