Fuchsian Groups and Continued Fractions

Year 2018, Volume: 10, 165 - 168, 29.12.2018

Nazlı Yazıcı Gözütok , İlgıt Zengin Bahadır Özgür Güler

Abstract

The suborbital graph is a directed graph arisen from the transitive group action. We investigate

suborbital graphs forming by the action of N_P(Gamma) which is the normalizer of modular group in the Picard group. We

give necessary and sufficient conditions for paired and self-paired graphs.

Keywords

Normalizer of the modular group, suborbital graphs, continued fraction

References

• Bigg NL, White AT Permutation groups and combinatorial structures. London Mathematical Society Lecture Note Series, 33, CUP, Cambridge,1979.
• Jones GA, Singerman D, Complex functions: an algebraic and geometric viewpoint, Cambridge University Press, Cambridge, 1987.
• Jones GA, Singerman D,Wicks K, The modular group and generalized Farey graphs. London Math. Soc. Lecture Note Series 160(1991):316–338.
• Kushwaha, S.; Sarma, R.; Continued fractions arising from F1;3. Ramanujan J. 46 (2018), no. 3, 605–631.
• Nathanson, M.B., A forest of linear fractional transformations. Int. J. Number Theory 11 (2015), no. 4, 1275–1299.
• Sarma R., Kushwaha S, Krishnan R, Continued fractions arising from F1;2. J. Number Theory 154(2015): 179–200.
• Sims C.C., Graphs and finite permutation groups, Math. Z., 95, (1967), 76-86.
• Olds C.D., Continued Fractions. New Mathematical Library. The Mathematical Association of America, Washington, 1963.
• Yazıcı Gözütok, N., Güler, B.Ö., Suborbital Graphs of the Normalizer of Modular Group in the Picard Group, Iran J Sci Technol Trans Sci(2017).