{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T05:47:01Z","timestamp":1723096021427},"reference-count":0,"publisher":"Combinatorial Press","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>In this article, we define \\(q\\)-generalized Fibonacci polynomials and \\(q\\)-generalized Lucas polynomials using \\(q\\)-binomial coefficient and obtain their recursive properties. In addition, we introduce generalized \\(q\\)-Fibonacci matrix and generalized \\(q\\)-Lucas matrix, then we derive their basic identities. We define \\((k,q,t)\\)-symmetric generalized Fibonacci matrix and \\((k,q,t)\\)-symmetric generalized Lucas matrix, then we give the Cholesky factorization of these matrices. Finally, we give determinantal and permanental representations of these new polynomial sequences.<\/jats:p>","DOI":"10.61091\/ars158-12","type":"journal-article","created":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:20Z","timestamp":1713134000000},"page":"117-128","source":"Crossref","is-referenced-by-count":0,"title":["\\(q\\)-Analogue of the Generalized Fibonacci and Lucas Polynomials"],"prefix":"10.61091","volume":"158","author":[{"name":"Faculty of Education, Tokat Gaziosmanpa\\c{s}a University, 60250 Tokat, Turkey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adem","family":"\u015eAHIN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:34Z","timestamp":1713134014000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-158\/q-analogue-of-the-generalized-fibonacci-and-lucas-polynomials\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2024,3,31]]},"published-print":{"date-parts":[[2024,3,31]]}},"URL":"https:\/\/doi.org\/10.61091\/ars158-12","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"type":"print","value":"0381-7032"},{"type":"electronic","value":"2817-5204"}],"subject":[],"published":{"date-parts":[[2024,1]]}}}