On the Norms of Circulant and r−r-Circulant Matrices With the Hyperharmonic Fibonacci Numbers

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

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 $\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers. We obtain spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers

GCD matrices, posets, and nonintersecting paths

We show that with any finite partially ordered set one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.Comment: 10 pages, see related papers at http://www.math.msu.edu/~saga

On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number

WOS: 000434277000016In this paper, we study the spectral norms of the geometric circulant matrices T-r* = Ctirc,*(T-0, T-1, . . . ,Tn-1) and the symmetric geometric circulant matrices STr* = SCirc(r)* (T-0, T-1, . . . ,Tn-1), where T-n denotes the nth Tribonacci number and r is any complex number

q - Bernoulli Matrices and Their Some Properties

WOS: 000421187900016In this study, we defineq - Bernoulli matrix B(q) and q-Bernoulli polynomial matrix B(x,q) by using q -Bernoulli numbers, and polynomials respectively. We obtain some properties of B (q) and B(x,q) We obtain factorizations q -Bernoulli polynomial matrix and shifted q -Bernoulli matrix using special matrices

Some Combinatorial Identities of q-Harmonic and q-Hyperharmonic Numbers

WOS: 000383001400001In this paper, by means of q-difference operator we derive q-analogue for several well known results for harmonic numbers. Also we give some identities concerning q-hyperharmonic numbers

On the bounds for the spectral norms of geometric circulant matrices

In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices