http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
RELATIONSHIPS BETWEEN CUSP POINTS IN THE EXTENDED MODULAR GROUP AND FIBONACCI NUMBERS
Koruoglu, Ozden,Sarica, Sule Kaymak,Demir, Bilal,Kaymak, A. Furkan The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.3
Cusp (parabolic) points in the extended modular group ${\bar{\Gamma}}$ are basically the images of infinity under the group elements. This implies that the cusp points of ${\bar{\Gamma}}$ are just rational numbers and the set of cusp points is $Q_{\infty}=Q{\cup}\{{\infty}\}$.The Farey graph F is the graph whose set of vertices is $Q_{\infty}$ and whose edges join each pair of Farey neighbours. Each rational number x has an integer continued fraction expansion (ICF) $x=[b_1,{\cdots},b_n]$. We get a path from ${\infty}$ to x in F as $<{\infty},C_1,{\cdots},C_n>$ for each ICF. In this study, we investigate relationships between Fibonacci numbers, Farey graph, extended modular group and ICF. Also, we give a computer program that computes the geodesics, block forms and matrix represantations.
Birol, Furkan,Koruoglu, Ozden,Sahin, Recep,Demir, Bilal The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
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.
One relator quotients of the extended modular group
S. Ikikardes,Ö. Koruoglu,R. Sahin,I. N. Cangül 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.17 No.2
In this paper, we obtain one relator quotients of the extended modular group by adding an extra relation to the existing two relations. Then, we show that some of one-relator quotients of ┍ are M-groups.
( Furkan Birol ),( Ozden Koruoglu ),( Recep Sahin ),( Bilal Demir ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
We consider the extended generalized Hecke groups H<sub>3;q</sub> generated by X(z) = -(z - 1)<sup>-1</sup>, Y (z) = -(z + λ<sub>q</sub>)<sup>-1</sup> with λ<sub>q</sub> =2 cos(π/q) where q ≥ 3 an integer. In this work, we study the generalized Pell sequences in H<sub>3;q</sub> : Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group H<sub>3;3</sub> can be written by using Pell, Pell-Lucas and modified-Pell numbers.