{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:02Z","timestamp":1753893782239,"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>Stanley conjectured that the number of maximal chains in the weak Bruhat order of $S_n$, or equivalently the number of reduced decompositions of the reverse of the identity permutation $ w_0 = n,n-1,n-2,\\ldots,2,1$, equals the number of standard Young tableaux of staircase shape $s=\\{n-1,n-2,\\ldots,1\\}$.  Originating from this conjecture remarkable connections between standard Young tableaux and reduced words have been discovered.  Stanley proved his conjecture algebraically, later Edelman and Greene found a bijective proof. We provide an extension of the Edelman and Greene bijection to a larger class of words. This extension is similar to the extension of the Robinson-Schensted correspondence to two line arrays. Our proof is inspired by Viennot's planarized proof of the Robinson-Schensted correspondence. As it is the case with the classical correspondence the planarized proofs have their own beauty and simplicity.<\/jats:p>","DOI":"10.37236\/1554","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:29Z","timestamp":1578708569000},"source":"Crossref","is-referenced-by-count":1,"title":["The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene"],"prefix":"10.37236","volume":"8","author":[{"given":"Stefan","family":"Felsner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2000,12,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:29Z","timestamp":1579324829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1554","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,12,29]]},"article-number":"R10"}}