Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 3
Generalized Fibonacci sequences related to the extended hecke groups and an application to the extended modular group
- Pages
- 325–332
- DOI
- —
Abstract
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 }.
Özet
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 }.