{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822864,"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>The combinatorics of reduced words and their commutation classes plays an important role in geometric representation theory. For a semisimple complex Lie group $G$, a string polytope is a convex polytope associated with each reduced word of the longest element $w_0$ in the Weyl group of $G$ encoding the character of a certain irreducible representation of $G$. In this paper, we deal with the case of type $A$, i.e., $G = \\mathrm{SL}_{n+1}(\\mathbb{C})$. A Gelfand\u2013\u2060Cetlin polytope is one of the most famous examples of string polytopes of type $A$. We provide a recursive formula enumerating reduced words of $w_0$ such that the corresponding string polytopes are combinatorially equivalent to a Gelfand\u2013\u2060Cetlin polytope. The recursive formula involves the number of standard Young tableaux of shifted shape. We also show that each commutation class is completely determined by a list of quantities called indices.<\/jats:p>","DOI":"10.37236\/10071","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T12:20:02Z","timestamp":1645705202000},"source":"Crossref","is-referenced-by-count":0,"title":["Enumeration of Gelfand\u2013\u2060Cetlin Type Reduced Words"],"prefix":"10.37236","volume":"29","author":[{"given":"Yunhyung","family":"Cho","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jang Soo","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eunjeong","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,2,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T12:20:03Z","timestamp":1645705203000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i1p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1,27]]}},"URL":"https:\/\/doi.org\/10.37236\/10071","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,2,11]]},"article-number":"P1.27"}}