Recep ŞAHİN, Ozden KORUOĞLU

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

The extended Hecke groups \overline{H}(l q) are generated by T(z)=-1/z, S(z)=-1/(z+l q) and R(z)=1/ \overline{z} with l q=2\cos (p /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{G }, in the extended Hecke groups \overline{H}(lq). Then we apply our results to \overline{G } to find all elements of the extended modular group \overline{G }.

Anahtar Kelimeler:

Extended Hecke groups, extended modular group, Fibonacci numbers

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

Keywords:

Extended Hecke groups, extended modular group, Fibonacci numbers,

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Balıkesir University, Necatibey Education Faculty, Balıkesir-TURKEY e-mail: ozdenk@balikesir.edu.tr Recep S¸AH˙IN Balıkesir University, Faculty of Arts and Science, Mathematics Department, 10145 Balıkesir-TURKEY e-mail: rsahin@balikesir.edu.tr