• Honam Mathematical Journal
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• v.41 no.1
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• pp.197-206
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• 2019

We consider the extended generalized Hecke groups ${\bar{H}}_{3,q}$ generated by $X(z)=-(z-1)^{-1}$, $Y(z)=-(z+{\lambda}_q)^{-1}$ with ${\lambda}_q=2\;cos({\frac{\pi}{q}})$ where $q{\geq}3$ an integer. In this work, we study the generalized Pell sequences in ${\bar{H}}_{3,q}$. Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group ${\bar{H}}_{3,3}$ can be written by using Pell, Pell-Lucas and modified-Pell numbers.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.365-378
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• 2004

The orders in quaternion algebras play central role in the theory of Hecke operators. In this paper, we study the order of two sided ideal group in orders of a quaternion algebra.

• East Asian mathematical journal
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• v.32 no.5
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• pp.717-728
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• 2016

In this paper, we give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.135-151
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• 2005

In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.