{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:22Z","timestamp":1753893862850,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A $\\mu$-way $k$-homogeneous Latin trade was defined by Bagheri Gh, Donovan, Mahmoodian (2012), where the existence of $3$-way $k$-homogeneous Latin trades was specifically investigated. We investigate the existence of a certain class of $\\mu$-way $k$-homogeneous Latin trades with an idempotent like property. We present a number of constructions for $\\mu$-way $k$-homogeneous Latin trades with this property, and show that these can be used to fill in the spectrum of $3$-way $k$-homogeneous Latin trades for all but $196$ possible exceptions.\u00a0<\/jats:p>","DOI":"10.37236\/5125","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:00:38Z","timestamp":1578697238000},"source":"Crossref","is-referenced-by-count":1,"title":["The Spectrum for $3$-Way $k$-Homogeneous Latin Trades"],"prefix":"10.37236","volume":"22","author":[{"given":"Trent G.","family":"Marbach","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lijun","family":"Ji","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:09:11Z","timestamp":1579255751000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5125","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,10,16]]},"article-number":"P4.1"}}