{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T15:31:20Z","timestamp":1775835080842,"version":"3.50.1"},"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>Suppose $P$ is a partially ordered set that is locally finite, has a least element, and admits a rank function. We call $P$ a weighted-relation poset if all the covering relations of $P$ are assigned a positive integer weight. We develop a theory of covering maps for weighted-relation posets, and in particular show that any weighted-relation poset $P$ has a universal cover $\\tilde P\\to P$, unique up to isomorphism, so that  1. $\\tilde P\\to P$ factors through any other covering map $P'\\to P$; 2. every principal order ideal of $\\tilde P$ is a chain; and 3. the weight assigned to each covering relation of $\\tilde P$ is 1.  If $P$ is a poset of \"natural\" combinatorial objects, the elements of its universal cover $\\tilde P$ often have a simple description as well. For example, if $P$ is the poset of partitions ordered by inclusion of their Young diagrams, then the universal cover $\\tilde P$ is the poset of standard Young tableaux; if $P$ is the poset of rooted trees ordered by inclusion, then $\\tilde P$ consists of permutations. We discuss several other examples, including the posets of necklaces, bracket arrangements, and compositions.<\/jats:p>","DOI":"10.37236\/1576","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:06:56Z","timestamp":1578708416000},"source":"Crossref","is-referenced-by-count":4,"title":["An Analogue of Covering Space Theory for Ranked Posets"],"prefix":"10.37236","volume":"8","author":[{"given":"Michael E.","family":"Hoffman","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,10,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:16:48Z","timestamp":1579324608000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,10,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1576","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,10,11]]},"article-number":"R32"}}