{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T04:29:46Z","timestamp":1775536186599,"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>We derive explicit expressions for the generating series of the fundamental  solutions of the $A_r$ quantum $Q$-system of Di Francesco and Kedem [ Non-commutative integrability, paths and quasi-determinants, Adv. in Math.  228(1) (2011) 97\u2013152], expressed in terms of any admissible initial data.  These involve products of quantum multinomial coefficients, coded by the initial  data structure.<\/jats:p>","DOI":"10.37236\/663","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:42:38Z","timestamp":1578714158000},"source":"Crossref","is-referenced-by-count":3,"title":["Quantum $A_r$ $Q$-System Solutions as q-Multinomial Series"],"prefix":"10.37236","volume":"18","author":[{"given":"Philippe Di","family":"Francesco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,9,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p176\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p176\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:02:21Z","timestamp":1579302141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/663","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,9]]},"article-number":"P176"}}