{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:20:41Z","timestamp":1759335641216,"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 study the shape of the Young diagram $\\lambda$ associated via the Robinson\u2013Schensted\u2013Knuth algorithm to a random permutation in $S_n$ such that the length of the longest decreasing subsequence is not bigger than a fixed number $d$; in other words we study the restriction of the Plancherel measure to Young diagrams with at most $d$ rows. We prove that in the limit $n\\to\\infty$ the rows of $\\lambda$ behave like the eigenvalues of a certain random matrix (namely the traceless Gaussian Unitary Ensemble random matrix) with $d$ rows and columns. In particular, the length of the longest increasing subsequence of such a random permutation behaves asymptotically like the largest eigenvalue of the corresponding random matrix.<\/jats:p>","DOI":"10.37236\/929","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:52:23Z","timestamp":1578700343000},"source":"Crossref","is-referenced-by-count":2,"title":["Permutations Without Long Decreasing Subsequences and Random Matrices"],"prefix":"10.37236","volume":"14","author":[{"given":"Piotr","family":"\u0160niady","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:05:01Z","timestamp":1579302301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/929","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,10]]},"article-number":"R11"}}