Generalized Fibonacci sequences related to the extended hecke groups and an application to the extended modular group

Authors

ÖZDEN KORUOĞLU
RECEP ŞAHİN

DOI

10.3906/mat-0902-33

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 }.

Keywords

Extended Hecke groups, extended modular group, Fibonacci numbers

First Page

325

Last Page

332

Recommended Citation

KORUOĞLU, ÖZDEN and ŞAHİN, RECEP (2010) "Generalized Fibonacci sequences related to the extended hecke groups and an application to the extended modular group," Turkish Journal of Mathematics: Vol. 34: No. 3, Article 3. https://doi.org/10.3906/mat-0902-33
Available at: https://journals.tubitak.gov.tr/math/vol34/iss3/3