{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:52Z","timestamp":1753893832294,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Lots of research focuses on the combinatorics behind various bases of cluster algebras.\u00a0This paper studies the natural basis of a type $A$ cluster algebra, which consists of all cluster monomials. We introduce a new kind of combinatorial formula for the cluster monomials in terms of the so-called globally compatible collections. We give bijective proofs of these formulas by comparing with the well-known combinatorial models of the $T$-paths and of the perfect matchings in a snake diagram. For cluster variables of a type $A$ cluster algebra, we give a bijection that relates our new formula with the theta functions constructed by Gross, Hacking, Keel and Kontsevich.<\/jats:p>","DOI":"10.37236\/6464","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:54:24Z","timestamp":1578671664000},"source":"Crossref","is-referenced-by-count":1,"title":["New Combinatorial Formulas for Cluster Monomials of Type $A$ Quivers"],"prefix":"10.37236","volume":"24","author":[{"given":"Kyungyong","family":"Lee","sequence":"first","affiliation":[]},{"given":"Li","family":"Li","sequence":"additional","affiliation":[]},{"given":"Ba","family":"Nguyen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,6,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:56:18Z","timestamp":1579236978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6464","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,6,16]]},"article-number":"P2.42"}}