Tuglu, Naim; Yesil, Fatma; Kocer, E. Gokcen; Dziemiańczuk, Maciej The \(F\)-analogue of Riordan representation of Pascal matrices via Fibonomial coefficients. (English) Zbl 1463.05021 J. Appl. Math. 2014, Article ID 841826, 6 p. (2014). Summary: We study an analogue of Riordan representation of Pascal matrices via Fibonomial coefficients. In particular, we establish a relationship between the Riordan array and Fibonomial coefficients, and we show that such Pascal matrices can be represented by an \(F\)-Riordan pair. Cited in 3 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 15B36 Matrices of integers 15A23 Factorization of matrices 05A10 Factorials, binomial coefficients, combinatorial functions PDF BibTeX XML Cite \textit{N. Tuglu} et al., J. Appl. Math. 2014, Article ID 841826, 6 p. (2014; Zbl 1463.05021) Full Text: DOI References: [1] Shapiro, L. W.; Getu, S.; Woan, W. J.; Woodson, L. C., The Riordan group, Discrete Applied Mathematics, 34, 1-3, 229-239 (1991) · Zbl 0754.05010 [2] Sprugnoli, R., Riordan arrays and combinatorial sums, Discrete Mathematics, 132, 1-3, 267-290 (1994) · Zbl 0814.05003 [3] Sprugnoli, R., Riordan arrays and the Abel-Gould identity, Discrete Mathematics, 142, 1-3, 213-233 (1995) · Zbl 0832.05007 [4] Kwasniewski, A. K., Fibonomial cumulative connection constants, Bulletin of the Institute of Combinatorics and Its Applications, 44, 81-92 (2005) · Zbl 1075.11010 [5] Krot, E., Further developments in finite fibonomial calculus [6] Knott, R., The Fibonomials [7] Call, G. S.; Velleman, D. J., Pascal’s matrices, The American Mathematical Monthly, 100, 4, 372-376 (1993) · Zbl 0788.05011 [8] Zhang, Z., The linear algebra of the generalized Pascal matrix, Linear Algebra and Its Applications, 250, 51-60 (1997) · Zbl 0873.15014 [9] Zhang, Z.; Wang, T., Generalized Pascal matrix and recurrence sequences, Linear Algebra and Its Applications, 283, 1-3, 289-299 (1998) · Zbl 1067.15502 [10] Zhang, Z.; Liu, M., An extension of the generalized Pascal matrix and its algebraic properties, Linear Algebra and Its Applications, 271, 169-177 (1998) · Zbl 0892.15018 [11] Zhang, Z.; Wang, X., A factorization of the symmetric Pascal matrix involving the Fibonacci matrix, Discrete Applied Mathematics, 155, 17, 2371-2376 (2007) · Zbl 1125.05023 [12] Lee, G.-y.; Cho, S.-H., The generalized Pascal matrix via the generalized Fibonacci matrix and the generalized Pell matrix, Journal of the Korean Mathematical Society, 45, 2, 479-491 (2008) · Zbl 1191.05015 [13] Barry, P., A study of integer sequences, Riordan arrays, Pascal-like arrays and Hankel transforms [14] Carlitz, L., Sequences and inversions, Duke Mathematical Journal, 37, 193-198 (1970) · Zbl 0206.02302 [15] Carlitz, L., \(q\)-Bernoulli and Eulerian numbers, Transactions of the American Mathematical Society, 76, 332-350 (1954) · Zbl 0058.01204 [16] Carlitz, L., Generating functions for powers of certain sequences of numbers, Duke Mathematical Journal, 29, 521-537 (1962) · Zbl 0147.02105 [17] Corcino, R. B., On \(p, q\)-binomial coefficients, Integers, 8, A29, 1-16 (2008) · Zbl 1210.05007 [18] Dziemiańczuk, M., First remark on a \(\zeta \)-analogue of the Stirling numbers, Integers, 11, A9, 1-10 (2011) · Zbl 1230.11024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.