{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:47Z","timestamp":1753893827370,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A Latin tableau of shape $\\lambda$ and type $\\mu$ is a Young diagram of shape $\\lambda$ in which each box contains a single positive integer, with no repeated integers in any row or column, and the $i$th most common integer appearing $\\mu_i$ times. Over twenty years ago, Chow et al., in their study of a generalization of Rota's basis conjecture that they called the wide partition conjecture, conjectured a necessary and sufficient condition for the existence of a Latin tableau of shape $\\lambda$ and type $\\mu$. We report some computational evidence for this conjecture, and prove that the conjecture correctly characterizes, for any given $\\lambda$, at least the first four parts of $\\mu$.<\/jats:p>","DOI":"10.37236\/13248","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T15:19:07Z","timestamp":1750346347000},"source":"Crossref","is-referenced-by-count":0,"title":["The Latin Tableau Conjecture"],"prefix":"10.37236","volume":"32","author":[{"given":"Timothy Y.","family":"Chow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark G.","family":"Tiefenbruck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,6,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T15:19:07Z","timestamp":1750346347000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,20]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/13248","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,6,20]]},"article-number":"P2.48"}}