Naim Tuglu

GCD matrices, posets, and nonintersecting paths

We show that with any finite partially ordered set P (which need not be a lattice) one can associate a matrix whose determinant factors nicely. This was also noted by D.A. Smith, although his proof uses manipulations in the incidence algebra of P while ours is combinatorial, using nonintersecting paths in a digraph. As corollaries, we obtain new proofs for and generalizations of a number of results in the literature about GCD matrices and their relatives.

On the representation of k-generalized Fibonacci and Lucas numbers

Abstract In this paper we give some determinantal and permanental representations of k-generalized Fibonacci and Lucas numbers. We obtain the Binet’s formula for these sequences by using our representations.

Bivariate fibonacci like p–polynomials

Abstract In this article, we study the bivariate Fibonacci and Lucas p –polynomials ( p xa0⩾xa00 is integer) from which, specifying x , y and p , bivariate Fibonacci and Lucas polynomials, bivariate Pell and Pell-Lucas polynomials, Jacobsthal and Jacobsthal–Lucas polynomials, Fibonacci and Lucas p –polynomials, Fibonacci and Lucas p –numbers, Pell and Pell–Lucas p –numbers and Chebyshev polynomials of the first and second kind, are obtained. Afterwards, we obtain some properties of the bivariate Fibonacci and Lucas p –polynomials.

Determinant and Inverse of Meet and Join Matrices

We define meet and join matrices on two subsets X and Y of a lattice (P, ) with respect to a complex-valued function f on P by (X ,Y) f = ( f (xi ∧ yi)) and [X ,Y] f = ( f (xi ∨ yi)), respectively. We present expressions for the determinant and the inverse of (X ,Y) f and [X ,Y] f , and as special cases we obtain several new and known formulas for the determinant and the inverse of the usual meet and join matrices (S) f and [S] f .

On the harmonic and hyperharmonic Fibonacci numbers

In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for Fn

Incomplete Bivariate Fibonacci and Lucas -Polynomials

mathbb{F}_{n}

On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers

, which is concerned with finite sums of reciprocals of Fibonacci numbers. We obtain the spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers.

The

We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers. On choosing 𝑥=1, 𝑦=2, we get the incomplete generalized Jacobsthal number and besides for 𝑝=1 the incomplete generalized Jacobsthal-Lucas numbers. In the case 𝑥=1, 𝑦=1, 𝑝=1, we have the incomplete Fibonacci and Lucas numbers. If 𝑥=1, 𝑦=1, 𝑝=1, 𝑘=⌊(𝑛−1)/(𝑝

F

In this paper, we study norms of circulant and r-circulant matrices involving harmonic Fibonacci and hyperharmonic Fibonacci numbers. We obtain inequalities by using matrix norms.

-Analogue of Riordan Representation of Pascal Matrices via Fibonomial Coefficients

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 -Riordan pair.