Gwang-Yeon Lee

k-Lucas numbers and associated bipartite graphs

For a positive integer k⩾2, the k-Fibonacci sequence {gn(k)} is defined as: g1(k)=⋯=gk−2(k)=0, gk−1(k)=gk(k)=1 and for n>k⩾2, gn(k)=gn−1(k)+gn−2(k)+⋯+gn−k(k). Moreover, the k-Lucas sequence {ln(k)} is defined as ln(k)=gn−1(k)+gn+k−1(k) for n⩾1. In this paper, we consider the relationship between gn(k) and ln(k) and 1-factors of a bipartite graph.

On Coincidence and Fixed-Point Theorems in Symmetric Spaces

We give an axiom (C.C) in symmetric spaces and investigate the relationships between (C.C) and axioms (W3), (W4), and (H.E). We give some results on coinsidence and fixed-point theorems in symmetric spaces, and also, we give some examples for the results of Imdad et al. (2006).

Some combinatorial identities via Fibonacci numbers

The Pascal matrix and the Stirling matrices of the first kind and the second kind obtained from the Fibonacci matrix are studied, respectively. Also, we obtain combinatorial identities from the matrix representation of the Pascal matrix, the Stirling matrices of the first kind and the second kind and the Fibonacci matrix.

Extremal properties of ray-nonsingular matrices

A ray-nonsingular matrix is a square complex matrix, A, such that each complex matrix whose entries have the same arguments as the corresponding entries of A, is nonsingular. Extremal properties of ray-nonsingular matrices are studied in this paper. Combinatorial and probabilistic arguments are used to prove that if the order of a ray-nonsingular matrix is at least 6, then it must contain a zero entry, and that if each of its rows and columns have an equal number, k, of nonzeros, then k613. c 2000 Elsevier Science B.V. All rights reserved.

On the K-generalized Fibonacci matrix Qk

Abstract The k- generalized Fibonacci sequence { g ( k ) n } is defined as follows: g ( k ) 1 = … = g ( k ) k − 2 = 0, g ( k ) k − 1 = g ( k ) k = 1, and for n > k ⩾ 2, g ( k ) n = g ( k ) n − 1 + g ( k ) n − 2 + … g ( k ) n − k . We consider the relationship between g ( k ) n and 1-factors of a bipartite graph and the eigenvalues of k- generalized Fibonacci matrix Q k for k ⩾ 2. We give some interesting examples in combinatorics and probability with respect to the k- generalized Fibonacci sequence.

The linear algebra of the k-Fibonacci matrix

Abstract For a positive integer k⩾2, the k-Fibonacci sequence {g(k)n} is defined as: g(k)1=⋯=g(k)k−2=0, g(k)k−1=g(k)k=1 and for n>k⩾2, g(k)n=g(k)n−1+g(k)n−2+⋯+g(k)n−k. The n×n k-Fibonacci matrix F (k) n =[f(k) ij ] n is defined as: for fixed k⩾2, f(k) ij = g i−j+1 i−j+1⩾0, 0 i−j+1 where gn=g(k)n+k−2. Also, the n by n k-symmetric Fibonacci matrix Q (k) n =[q(k) ij ] n is defined as q(k) ij =q(k) ji = ∑ l=1 k q(k) i,j−l i+1⩽j, ∑ l=1 k q(k) i,i−l +g 1 i=j, where q(k)ij=0 for j⩽0. If k=2, then F (2) n is the Fibonacci matrix and Q (2) n is the symmetric Fibonacci matrix. The properties of the Fibonacci matrix and the symmetric Fibonacci matrix are well-known. In this paper, we discuss the linear algebra of the k-Fibonacci matrix and the symmetric k-Fibonacci matrix.

THE GENERALIZED PASCAL MATRIX VIA THE GENERALIZED FIBONACCI MATRIX AND THE GENERALIZED PELL MATRIX

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

L-topological meet theorems

Kindler gave a purely topological condition for an intersection of subsets of some set to be nonempty, which plays an important role in topology. This paper generalizes Kindlers theorems to the fuzzy lattice-based setting, due to a proper choice of compactness and connectedness axioms. It shows that almost all basic results of Kindler survive in the extended setting.

Linear transformations that preserve the assignment

Abstract Let R = (r1,…,rn) and S = (s1,…,sn) be vectors of positive integers. Let U (R,S) be the set of (0,1) matrices with row sums ri and column sums sj, i, j = 1,…,n. Let X be a real matrix of order n. The (R,S) assignment function PR,S(·) is defined by P R,S (X)= ∑ AϵU(R,S) (i,j)ϵ supp (A) π xij , where supp(A) = {(i,j) : aij ≠ 0}. We investigate the structure of linear transformations on the set of real matrices Mn(R) into itself such that PR,S(X) = PR,S(T(X)).

A characterization of the nearly sign central matrices and its minimallity

The sign central matrices were characterized by Ando and Brualdi. And, the nearly sign central matrices were characterized by Lee and Cheon. In this paper, we give another characterization of nearly sign central matrices. Also, we introduce the nearly minimal sign central matrices and study the properties of nearly minimal sign central matrices.