{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:08:17Z","timestamp":1767236897938,"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 give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length $n$ and the number of occurrences of the dashed pattern 32\u20131 in permutations on $[n]$. We introduce the  inversion number of a permutation tableau. For a permutation tableau $T$ and the permutation $\\pi$ obtained from $T$ by the bijection of Corteel and Nadeau, we show that the inversion number of $T$ equals the number of occurrences of the dashed pattern 32\u20131 in the reverse complement of $\\pi$. We also show that permutation tableaux without inversions coincide with L-Bell tableaux introduced by Corteel and Nadeau.<\/jats:p>","DOI":"10.37236\/598","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:47:30Z","timestamp":1578714450000},"source":"Crossref","is-referenced-by-count":4,"title":["Permutation Tableaux and  the Dashed Permutation Pattern 32&amp;ndash;1"],"prefix":"10.37236","volume":"18","author":[{"given":"William Y.C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Lewis H.","family":"Liu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,5,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p111\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p111\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:12:02Z","timestamp":1579302722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/598","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,5,16]]},"article-number":"P111"}}