{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:43Z","timestamp":1759335943177,"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>Sylvester's identity is a classical determinantal identity with a simple linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a $\\beta$-extension that is both a generalization of Sylvester's identity and the $\\beta$-extension of the quantum MacMahon master theorem.<\/jats:p>","DOI":"10.37236\/960","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:50:39Z","timestamp":1578718239000},"source":"Crossref","is-referenced-by-count":2,"title":["Non-Commutative Sylvester's Determinantal Identity"],"prefix":"10.37236","volume":"14","author":[{"given":"Matja\u017e","family":"Konvalinka","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,5,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:02:49Z","timestamp":1579320169000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/960","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,5,31]]},"article-number":"R42"}}