{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841077,"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 study the equivalence relation on the set of acyclic orientations of an undirected graph $\\Gamma$ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in turn, the admissible sequences. This allows us to construct an explicit bijection from the equivalence classes over $\\Gamma$ to those over $\\Gamma'$ and $\\Gamma\"$, the graphs obtained from $\\Gamma$ by edge deletion and edge contraction of a fixed cycle-edge, respectively.  This bijection yields quick and elegant proofs of two non-trivial results: $(i)$ A complete combinatorial invariant of the equivalence classes, and $(ii)$ a solution to the conjugacy problem of Coxeter elements for simply-laced Coxeter groups. The latter was recently proven by H. Eriksson and K. Eriksson using a much different approach.<\/jats:p>","DOI":"10.37236\/684","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:41:16Z","timestamp":1578714076000},"source":"Crossref","is-referenced-by-count":7,"title":["Posets from Admissible Coxeter Sequences"],"prefix":"10.37236","volume":"18","author":[{"given":"Matthew","family":"Macauley","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henning S.","family":"Mortveit","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,10,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p197\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p197\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:01:11Z","timestamp":1579302071000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/684","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,3]]},"article-number":"P197"}}