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Full-Text Articles in Physical Sciences and Mathematics
Relation Between Matrices And The Suborbital Graphs By The Special Number Sequences, Ümmügülsün Akbaba, Ali̇ Hi̇kmet Değer
Relation Between Matrices And The Suborbital Graphs By The Special Number Sequences, Ümmügülsün Akbaba, Ali̇ Hi̇kmet Değer
Turkish Journal of Mathematics
under circuit and forest conditions. Special number sequences and special vertex values of minimal length paths in suborbital graphs have been associated in our previous studies. In these associations, matrix connections of the special continued fractions $\mathcal K (-1/-k)$, where $k\in \mathbb{Z}^{+}, \ k\geq 2$ with the values of the special number sequences are used and new identities are obtained. In this study, by producing new matrices, new identities related to Fibonacci, Lucas, Pell, and Pell-Lucas number sequences are found by using both recurrence relations and matrix connections of the continued fractions. In addition, the farthest vertex values of the …
On Parabolic And Elliptic Elements Of The Modular Group, Bi̇lal Demi̇r, Özden Koruoğlu
On Parabolic And Elliptic Elements Of The Modular Group, Bi̇lal Demi̇r, Özden Koruoğlu
Turkish Journal of Mathematics
The modular group $\Gamma=PSL(2, \mathbf{Z})$ is isomorphic to the free product of two cyclic groups of orders $2$ and $3$. In this paper, we give a necessary and sufficient condition for the existence of elliptic and parabolic elements in $\Gamma$ with a given cusp point. Then we give an algorithm to obtain such elements in words of generators using continued fractions and paths in the Farey graph.