{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:35:17Z","timestamp":1759941317193,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>This paper completes the project of constructing combinatorial models (called frameworks) for the exchange graph and $\\mathbf{g}$-vector fan associated to any exchange matrix $B$ whose Cartan companion is of finite or affine type, using the combinatorics and geometry of Coxeter-sortable elements and Cambrian lattices\/fans. Specifically, we construct a framework in the unique non-acyclic affine case, the cyclically oriented $n$-cycle. In the acyclic affine case, a framework was constructed by combining a copy of the Cambrian fan for $B$ with an antipodal copy of the Cambrian fan for $-B$. In this paper, we extend this \"doubled Cambrian fan'' construction to the oriented $n$-cycle, using a more general notion of sortable elements for quivers with cycles. <\/jats:p>","DOI":"10.37236\/5387","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:19:22Z","timestamp":1578694762000},"source":"Crossref","is-referenced-by-count":1,"title":["A Cambrian Framework for the Oriented Cycle"],"prefix":"10.37236","volume":"22","author":[{"given":"Nathan","family":"Reading","sequence":"first","affiliation":[]},{"given":"David E","family":"Speyer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,12,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:37:41Z","timestamp":1579239461000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,23]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5387","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,12,23]]},"article-number":"P4.46"}}