{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829369,"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>We show that for any Latin square $L$ of order $2m$, we can partition the rows and columns of $L$ into pairs so that at most $(m+3)\/2$ of the $2\\times 2$ subarrays induced contain a repeated symbol. We conjecture that any Latin square of order $2m$ (where $m\\geq 2$, with exactly five transposition class exceptions of order $6$) has such a partition so that\u00a0 every $2\\times 2$ subarray induced contains no repeated symbol. We verify this conjecture by computer when $m\\leq 4$.<\/jats:p>","DOI":"10.37236\/2372","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:58:29Z","timestamp":1578693509000},"source":"Crossref","is-referenced-by-count":0,"title":["Induced Subarrays of Latin Squares Without Repeated Symbols"],"prefix":"10.37236","volume":"20","author":[{"given":"R. Julian R.","family":"Abel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicholas J.","family":"Cavenagh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaromy","family":"Kuhl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,3,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:25:56Z","timestamp":1579242356000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2372","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,1]]},"article-number":"P44"}}