{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:26Z","timestamp":1753893806885,"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>Let $\\mu$ be a partition of $k$, and $T$ a standard Young tableau of shape $\\mu$.  McKay, Morse, and Wilf show that the probability a randomly chosen Young tableau of $N$ cells contains $T$ as a subtableau is asymptotic to $f^\\mu\/k!$ as $N$ goes to infinity, where $f^\\mu$ is the number of all tableaux of shape $\\mu$.  We use a random-walk argument to show that the analogous asymptotic probability for randomly chosen Young tableaux with at most $n$ rows is proportional to $\\prod_{1\\le i &lt; j\\le n}\\bigl((\\mu_i-i)-(\\mu_j-j)\\bigr)$; as $n$ goes to infinity, the probabilities approach $f^\\mu\/k!$ as expected.  We have a similar formula for up-down tableaux; the probability approaches $f^\\mu\/k!$ if $\\mu$ has $k$ cells and thus the up-down tableau is actually a standard tableau, and approaches 0 if $\\mu$ has fewer than $k$ cells.<\/jats:p>","DOI":"10.37236\/1886","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:16:46Z","timestamp":1578701806000},"source":"Crossref","is-referenced-by-count":2,"title":["Asymptotics for the Distributions of Subtableaux in Young and Up-Down Tableaux"],"prefix":"10.37236","volume":"11","author":[{"given":"David J.","family":"Grabiner","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,4,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r29\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:17:16Z","timestamp":1579303036000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2r29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4,11]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1886","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,4,11]]},"article-number":"R29"}}