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    Bivariate Fibonacci and Lucas Like Polynomials
    (Gazi Univ, 2016) Kocer, E. Gokcen; Tuncez, Serife
    In this article, we study the generalized bivariate Fibonacci (GBF) and generalized bivariate Lucas (GBL) polynomials from specifying p(x,y) and q(x,y), classical bivariate Fibonacci and Lucas polynomials ((p(x,y)=x and q(x,y)=y). Afterwards, we obtain the some properties of the GBF and GBL polynomials.
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    The F-Analogue of Riordan Representation of Pascal Matrices via Fibonomial Coefficients
    (Hindawi Publishing Corporation, 2014) Tuglu, Naim; Yesil, Fatma; Kocer, E. Gokcen; Dziemianczuk, Maciej
    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.
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    Generalized Hybrid Fibonacci and Lucas p-numbers
    (Indian Nat Sci Acad, 2022) Kocer, E. Gokcen; Alsan, Huriye
    The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. Until this time, many researchers have studied related to hybrid numbers. In this paper, using the generalized Fibonacci and Lucas p-numbers, we introduce the generalized hybrid Fibonacci and Lucas p-numbers. Also, we give some special cases and algebraic properties of the generalized hybrid Fibonacci and Lucas p-numbers.
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    THE GRAM AND HANKEL MATRICES VIA SPECIAL NUMBER SEQUENCES
    (Honam Mathematical Soc, 2023) Alp, Yasemin; Kocer, E. Gokcen
    In this study, we consider the Hankel and Gram matrices which are defined by the elements of special number sequences. Firstly, the eigenvalues, determinant, and norms of the Hankel matrix defined by special number sequences are obtained. Afterwards, using the relationship between the Gram and Hankel matrices, the eigenvalues, determinants, and norms of the Gram matrices defined by number sequences are given.
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    Hybrid Leonardo numbers
    (Pergamon-Elsevier Science Ltd, 2021) Alp, Yasemin; Kocer, E. Gokcen
    Until today, many researchers have studied related to hybrid numbers which are a generalization of complex, hyperbolic and dual numbers. In this paper, using the Leonardo numbers, we introduce the hybrid Leonardo numbers. Also, we give some algebraic properties of the hybrid Leonardo numbers such as recurrence relation, generating function, Binet's formula, sum formulas, Catalan's identity and Cassini's identity. (c) 2021 Elsevier Ltd. All rights reserved.
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    The identities for generalized Fibonacci numbers via orthogonal projection
    (Bulgarian Acad Science, 2019) Alp, Yasemin; Kocer, E. Gokcen
    In this paper, we consider the space R(p, 1) of generalized Fibonacci sequences and orthogonal bases of this space. Using these orthogonal bases, we obtain the orthogonal projection onto a subspace R(p, 1) of R-n. By using the orthogonal projection, we obtain the identities for the generalized Fibonacci numbers.