{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:14:05Z","timestamp":1758824045605,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Linked partitions were introduced by Dykema\u00a0in the study of transforms in free probability theory, whereas permutation tableaux were introduced by Steingr\u00edmsson and Williams in the study of totally positive Grassmannian cells. Let $[n]=\\{1,2,\\ldots,n\\}$. Let $L(n,k)$ denote the set of\u00a0 linked partitions of $[n]$ with $k$ blocks, let $P(n,k)$ denote the set of\u00a0 permutations of $[n]$ with $k$ descents, and let $T(n,k)$ denote the set of permutation tableaux of length $n$ with $k$ rows. Steingr\u00edmsson and Williams found a bijection between the set of permutation tableaux of length $n$ with $k$ rows and the set of permutations of $[n]$ with $k$ weak excedances. Corteel and Nadeau gave a bijection between the set of permutation tableaux of length $n$ with $k$ columns and the set of permutations of $[n]$ with $k$ descents. In this paper, we establish a bijection between $L(n,k)$ and $P(n,k-1)$ and a bijection between $L(n,k)$ and $T(n,k)$. Restricting\u00a0the latter bijection to\u00a0 noncrossing linked partitions and nonnesting linked partitions, we find that the corresponding\u00a0 permutation tableaux\u00a0can be characterized by pattern avoidance.<\/jats:p>","DOI":"10.37236\/3408","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:21:42Z","timestamp":1578705702000},"source":"Crossref","is-referenced-by-count":1,"title":["Linked Partitions and Permutation Tableaux"],"prefix":"10.37236","volume":"20","author":[{"given":"William Y.C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Lewis H.","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Carol J.","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,9,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:12:33Z","timestamp":1579259553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,26]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/3408","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,9,26]]},"article-number":"P53"}}