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Generalized Pell sequences related to the extended generalized Hecke groups \({\overline{H}}_{3,q}\) and an application to the group \({\overline{H}}_{3,3}\). (English) Zbl 1423.20059

Summary: We consider the extended generalized Hecke groups \({\overline{H}}_{3,q}\) generated by \(X(z)=-(z-1)^{-1}, Y(z)=-(z+{\lambda}_q)^{-1}\) with \({\lambda}_q=2\;cos({\frac{\pi}{q}})\) where \(q\geq 3\) an integer. In this work, we study the generalized Pell sequences in \({\overline{H}}_{3,q}\). Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group \({\overline{H}}_{3,3}\) can be written by using Pell, Pell-Lucas and modified-Pell numbers.

MSC:

20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
11F06 Structure of modular groups and generalizations; arithmetic groups
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
Full Text: DOI

References:

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