{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T20:48:01Z","timestamp":1773262081209,"version":"3.50.1"},"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>Let $U$ be a matrix chosen randomly, with respect to Haar measure, from the unitary group $U(d).$ For any $k \\leq d,$ and any $k \\times k$ submatrix $U_k$ of $U,$ we express the average value of $|{\\rm Tr}(U_k)|^{2n}$ as a sum over partitions of $n$ with at most $k$ rows whose terms count certain standard and semistandard Young tableaux.  We combine our formula with a variant of the Colour-Flavour Transformation of lattice gauge theory to give a combinatorial expansion of an interesting family of unitary matrix integrals.  In addition, we give a simple combinatorial derivation of the moments of a single entry of a random unitary matrix, and hence deduce that the rescaled entries converge in moments to standard complex Gaussians. Our main tool is the Weingarten function for the unitary group.<\/jats:p>","DOI":"10.37236\/939","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:54:17Z","timestamp":1578718457000},"source":"Crossref","is-referenced-by-count":11,"title":["Truncations of Random Unitary Matrices and Young Tableaux"],"prefix":"10.37236","volume":"14","author":[{"given":"J.","family":"Novak","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,2,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:26:25Z","timestamp":1579321585000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/939","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,2,7]]},"article-number":"R21"}}