{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T11:18:02Z","timestamp":1648811882069},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"We characterize all permutations on even-by-even grids that maximally separate neighboring vertices. More precisely, let $n_1$, $n_2$ be positive even integers, let $I(n_1,n_2)=\\{1,\\dots,n_1\\}\\times\\{1,\\dots,n_2\\}$ be the $n_1\\times n_2$ grid, let $\\mathrm{d}$ be the $L_1$ metric on $I(n_1,n_2)$, and let $N=\\{\\{x,y\\}\\in I(n_1,n_2)\\times I(n_1,n_2): \\mathrm{d}(x,y)=1\\}$ be the set of neighbors in $I(n_1,n_2)$. We characterize all permutations $\\pi$ of $I(n_1,n_2)$ that maximize $\\sum_{\\{x,y\\}\\in N} \\mathrm{d}(\\pi(x),\\pi(y))$.<\/jats:p>","DOI":"10.37236\/8148","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:08:28Z","timestamp":1578640108000},"source":"Crossref","is-referenced-by-count":0,"title":["Permutations in Two Dimensions that Maximally Separate Neighbors"],"prefix":"10.37236","volume":"26","author":[{"given":"Mohammed","family":"Albow","sequence":"first","affiliation":[]},{"given":"Jeffrey","family":"Edgington","sequence":"additional","affiliation":[]},{"given":"Mario","family":"Lopez","sequence":"additional","affiliation":[]},{"given":"Petr","family":"Vojt\u011bchovsk\u00fd","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,4,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p1\/7813","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p1\/7813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:15:07Z","timestamp":1579234507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"http:\/\/dx.doi.org\/10.37236\/8148","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,5]]}}}