{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:22Z","timestamp":1753893802181,"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>Bergeron, Bousquet-M\u00e9lou and Dulucq [Ann. Sci. Math. Qu\u00e9bec 19 (1995), 139\u2013151] enumerated paths in the Hasse diagram of the following poset: the underlying set is that of all compositions, and a composition $\\mu$ covers another composition $\\lambda$ if $\\mu$ can be obtained from $\\lambda$ by adding $1$ to one of the parts of $\\lambda$, or by inserting a part of size $1$ into $\\lambda$. We employ the methods they developed in order to study the same problem for the following poset, which is of interest because of its relation to non-commutative term orders : the underlying set is the same, but $\\mu$ covers $\\lambda$ if $\\mu$ can be obtained from $\\lambda$ by adding $1$ to one of the parts of $\\lambda$, or by inserting a part of size $1$ at the left or at the right of $\\lambda$. We calculate generating functions for standard paths of fixed width and for standard paths of height $\\le 2$.<\/jats:p>","DOI":"10.37236\/1829","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:31:30Z","timestamp":1578691890000},"source":"Crossref","is-referenced-by-count":3,"title":["Standard Paths in Another Composition Poset"],"prefix":"10.37236","volume":"11","author":[{"given":"Jan","family":"Snellman","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,10,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r76\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r76\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:53:10Z","timestamp":1579305190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r76"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1829","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,10,26]]},"article-number":"R76"}}