Turkish Journal of Mathematics
Abstract
The extended Hecke groups \overline{H}(\lambda _{q}) are generated by T(z)=-1/z, S(z)=-1/(z+\lambda _{q}) and R(z)=1/ \overline{z} with \lambda _{q}=2\cos (\pi /q) for q\geq 3 integer. In this paper, we obtain a sequence which is a generalized version of the Fibonacci sequence given in [6] for the extended modular group \overline{\Gamma }, in the extended Hecke groups \overline{H}(\lambda_{q}). Then we apply our results to \overline{\Gamma } to find all elements of the extended modular group \overline{\Gamma }.
DOI
10.3906/mat-0902-33
Keywords
Extended Hecke groups, extended modular group, Fibonacci numbers
First Page
325
Last Page
332
Recommended Citation
KORUOĞLU, Ö, & ŞAHİN, R (2010). Generalized Fibonacci sequences related to the extended hecke groups and an application to the extended modular group. Turkish Journal of Mathematics 34 (3): 325-332. https://doi.org/10.3906/mat-0902-33
