• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.249-254
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• 2007

In this paper, we consider the embedding problem of postorder Fibonacci circulant. We show that Fibonacci linear array, Fibonacci mesh, Fibonacci tree, Fibonacci cubes and Hypercube are a subgraph of postorder Fibonacci circulant.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.231-240
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• 2005

We examine the Fibonacci length of certain centro-polyhedral groups and show that in some cases the lengths depend on tribonacci sequences. Further we obtain specific examples of infinite families of three-generator groups with constant, linear and (3-step) Wall number dependent Fibonacci lengths.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.675-683
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• 2016

We give the representation of Fibonacci quaternions for convenient calculus. We research the corresponding properties of Fibonacci quaternions and some examples of a function with values in modified Fibonacci quaternions.

• Annual Conference of KIPS
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• 2006.05a
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• pp.743-746
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• 2006

In this paper, we propose and analyze a new parallel computer topology, called the Fibonacci posterorder circulants. It connects ${\Large f}_x,\;n{\geq}2$ processing nodes, same the number of nodes used in a comparable Fibonacci cube. Yet its diameter is only ${\lfloor}\frac{n}{3}{\rfloor}$ almost one third that of the Fibonacci cube. Fibonacci cube is asymmetric, but it is a regular and symmetric static interconnection networks for large-scale, loosely coupled systems. It includes scalability and Fibonacci cube as a spanning subgraph.

• The KIPS Transactions:PartA
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• v.15A no.1
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• pp.27-34
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• 2008

In this paper, We propose a new parallel computer topology, called the Postorder Fibonacci Circulants and analyze its properties. It is compared with Fibonacci cubes, when its number of nodes is kept the same of comparable one. Its diameter is improved from n-2 to $[\frac{n}{3}]$ and its topology is changed from asymmetric to symmetric. It includes Fibonacci cube as a spanning graph.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.447-450
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• 2016

Let $F_n$ and $L_n$ be the nth Fibonacci number and Lucas number, respectively. The order of appearance of m in the Fibonacci sequence, denoted by z(m), is the smallest positive integer k such that m divides $F_k$. Marques obtained the formula of $z(L^k_n)$ in some cases. In this article, we obtain the formula of $z(L^k_n)$ for all $n,k{\geq}1$.

• Proceedings of the IEEK Conference
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• 2001.06c
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• pp.63-66
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• 2001

In this paper, We propose the new interconnection network which is designed to edge numbering labeling using postorder traversal which can reduce diameter when it has same node number with Hypercube, which can reduce total node numbers considering node degree and diameter on Fibonacci trees and its jump sequence of circulant is Fibonacci numbers. It has a simple (shortest oath)routing algorithm, diameter, node degree. It has a spaning subtree which is Fibonacci tree and it is embedded to Fibonacci tree. It is compared with Hypercube. We improve diameter compared with Hypercube.

• Journal for History of Mathematics
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• v.28 no.3
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• pp.151-164
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• 2015

The purpose of this paper is to develop a teaching and learning material integrated two subjects Pythagorean theorem and Fibonacci numbers. Traditionally the former subject belongs to geometry area and the latter is in algebra area. In this work we integrate these two issues and make a discovery method to generate infinitely many Pythagorean numbers by means of Fibonacci numbers. We have used this article as a teaching and learning material for a science high school and found that it is very appropriate for those students in advanced geometry and number theory courses.

• School Mathematics
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• v.12 no.4
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• pp.619-638
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• 2010

In this paper, we listed and reviewed some properties on polygonal numbers, pyramidal numbers and Pascal's triangle, and Fibonacci sequence. We discussed that the properties of gnomonic numbers, polygonal numbers and pyramidal numbers are explained integratively by introducing the generalized k-dimensional pyramidal numbers. And we also discussed that the properties of those numbers and relationships among generalized k-dimensional pyramidal numbers, Pascal's triangle and Fibonacci sequence are suitable for teaching and learning of mathematical reasoning and connections.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.171-180
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• 2006

Two infinite classes of special finite groups considered (The group G is special, if G' and Z(G) coincide). Using certain sequences of numbers we give explicit formulas for the Fibonacci lenghts of these classes which involve the well-known Wall numbers k(n).