{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:27Z","timestamp":1753893807300,"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>In a 1989 paper, Hanlon and Wales showed that the algebra structure of the Brauer Centralizer Algebra $A_f^{(x)}$ is completely determined by the ranks of certain combinatorially defined square matrices $Z^{\\lambda \/ \\mu}$, whose entries are polynomials in the parameter $x$.  We consider a set of matrices $M^{\\lambda \/ \\mu}$ found by Jockusch that have a similar combinatorial description.  These new matrices can be obtained from the original matrices by extracting the terms that are of \"highest degree\" in a certain sense. Furthermore, the $M^{\\lambda \/ \\mu}$ have analogues ${\\cal M}^{\\lambda \/ \\mu}$ that play the same role that the $Z^{\\lambda \/ \\mu}$ play in $A_f^{(x)}$, for another algebra that arises naturally in this context. We find very simple formulas for the determinants of the matrices $M^{\\lambda\/\\mu}$ and ${\\cal M}^{\\lambda \/ \\mu}$, which prove Jockusch's original conjecture that $\\det M^{\\lambda \/ \\mu}$ has only integer roots.  We define a Jeu de Taquin algorithm for standard matchings, and compare this algorithm to the usual Jeu de Taquin algorithm defined by Sch\u00fctzenberger for standard tableaux.  The formulas for the determinants of $M^{\\lambda\/\\mu}$ and ${\\cal M}^{\\lambda \/ \\mu}$ have elegant statements in terms of this new Jeu de Taquin algorithm.<\/jats:p>","DOI":"10.37236\/1217","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:25:33Z","timestamp":1578687933000},"source":"Crossref","is-referenced-by-count":0,"title":["Matrices connected with Brauer's centralizer algebras"],"prefix":"10.37236","volume":"2","author":[{"given":"Mark D.","family":"McKerihan","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,10,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T01:21:05Z","timestamp":1579310465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1217","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,10,31]]},"article-number":"R23"}}