{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:37:11Z","timestamp":1760027831975,"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 $B$ be a Ferrers board, i.e., the board obtained by  removing the Ferrers diagram of a partition from the top right corner of an  $n\\times n$ chessboard.  We consider a Markov chain on the set $R$ of rook  placements on $B$ in which you can move from one placement to any other legal  placement obtained by switching the columns in which two rooks sit.   We give sharp estimates for the rate of convergence of this Markov chain using  spectral methods.  As part of this analysis we give a complete combinatorial description of the eigenvalues of the transition matrix  for this chain.  We show that two extremes cases of this Markov chain correspond  to random walks on groups which are analyzed in the literature.   Our estimates for rates of convergence interpolate between those two results.<\/jats:p>","DOI":"10.37236\/1284","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:51:23Z","timestamp":1578689483000},"source":"Crossref","is-referenced-by-count":5,"title":["A random walk on the rook placements on a Ferrer's board"],"prefix":"10.37236","volume":"3","author":[{"given":"Phil","family":"Hanlon","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,2,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T01:17:59Z","timestamp":1579310279000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i2r26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,2,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[1996,1,24]]}},"URL":"https:\/\/doi.org\/10.37236\/1284","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1996,2,1]]},"article-number":"R26"}}