{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T01:02:10Z","timestamp":1779757330752,"version":"3.53.1"},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T00:00:00Z","timestamp":1778112000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,5,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we introduce and investigate a new class of Pascal-like matrices constructed using double F-factorial binomial coefficients, in which the standard factorial function is replaced by the Fibonacci factorial. We first define the double F-factorial binomial coefficient and employ it to generate a bivariate polynomial sequence incorporating both Fibonacci and Lucas factorial terms. Fundamental recurrence relations for the coefficients of these polynomials are established. Using these relations, we construct a $F$-Pascal-like matrix, denoted by $P_{t}\\left ( u,v\\right )_{F},$ and derive several of its algebraic properties, including matrix factorization, power identities, and determinant-trace relationships. We further define a new functional matrix $Q_{t,\\lambda }\\left ( x,y\\right )_{F},$ referred to as the $F$ -Pascal-like matrix, and include its additive and product properties. The proposed constructions extend classical binomial and Pascal matrices within the framework of Fibonacci analysis, providing potential applications in combinatorics, number theory, and matrix theory.<\/jats:p>","DOI":"10.1093\/jigpal\/jzag019","type":"journal-article","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T11:38:23Z","timestamp":1774957103000},"source":"Crossref","is-referenced-by-count":0,"title":["Fibonacci-based Pascal-like matrices with double factorial binomial structure"],"prefix":"10.1093","volume":"34","author":[{"given":"Can","family":"Kizilate\u015f","sequence":"first","affiliation":[{"name":"Department of Mathematics , Faculty of Science, Zonguldak B\u00fclent Ecevit University, 67100, Zonguldak, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nazlihan","family":"Terzio\u011flu","sequence":"additional","affiliation":[{"name":"Graduate School of Natural and Applied Sciences , Zonguldak B\u00fclent Ecevit University, 67100, Zonguldak, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,7]]},"reference":[{"key":"2026052520021041100_ref1","first-page":"1343","article-title":"Fibonacci and Lucas Pascal triangles","volume":"45","author":"Belbachir","year":"2016","journal-title":"Hacet J Math Stat"},{"key":"2026052520021041100_ref2","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1080\/00029890.1993.11990415","article-title":"Pascal\u2019s matrices","volume":"100","author":"Call","year":"1993","journal-title":"Am Math Mon"},{"key":"2026052520021041100_ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-2196-8","volume-title":"Advanced Combinatorics: The Art of Finite and Infinite Expansions","author":"Comtet","year":"1974"},{"key":"2026052520021041100_ref4","doi-asserted-by":"publisher","first-page":"177","DOI":"10.4169\/math.mag.85.3.177","article-title":"Double fun with double factorials","volume":"85","author":"Gould","year":"2012","journal-title":"Math Mag"},{"key":"2026052520021041100_ref5","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s13226-023-00496-x","article-title":"Pascal-like matrix with double factorial binomial coefficients","volume":"56","author":"Kizilaslan","year":"2025","journal-title":"Indian J Pure Appl Math"},{"key":"2026052520021041100_ref6","volume-title":"Fibonacci and Lucas Numbers With Applications","author":"Koshy","year":"2019"},{"key":"2026052520021041100_ref7","doi-asserted-by":"publisher","first-page":"754","DOI":"10.2478\/BF02475975","article-title":"An introduction to finite fibonomial calculus","volume":"2","author":"Krot","year":"2004","journal-title":"Centr Eur J Math"},{"key":"2026052520021041100_ref8","first-page":"163","article-title":"Generalized double Fibonomial numbers","volume":"40","author":"Shah","year":"2021","journal-title":"Ratio Math"},{"key":"2026052520021041100_ref9","doi-asserted-by":"publisher","first-page":"260","DOI":"10.2307\/3026776","article-title":"Binomial matrices","volume":"8","author":"Strum","year":"1977","journal-title":"Two-Year Coll Math J"},{"key":"2026052520021041100_ref10","doi-asserted-by":"crossref","first-page":"841826","DOI":"10.1155\/2014\/841826","article-title":"The $F$-analogue of Riordan representation of Pascal matrices via Fibonomial coefficients","volume":"2014","author":"Tuglu","year":"2014","journal-title":"J Appl Math"},{"key":"2026052520021041100_ref11","doi-asserted-by":"publisher","first-page":"2629","DOI":"10.1080\/03081087.2020.1809619","article-title":"The linear algebra of a Pascal-like matrix","volume":"70","author":"Zheng","year":"2022","journal-title":"Linear Multilinear A"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/34\/3\/jzag019\/68247371\/jzag019.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/34\/3\/jzag019\/68247371\/jzag019.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T00:02:17Z","timestamp":1779753737000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/doi\/10.1093\/jigpal\/jzag019\/8672628"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,7]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,5,26]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzag019","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,6]]},"published":{"date-parts":[[2026,5,7]]},"article-number":"jzag019"}}