Some group actions and Fibonacci numbers
Yıl: 2022 Cilt: 71 Sayı: 1 Sayfa Aralığı: 273 - 284 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.939096 İndeks Tarihi: 29-07-2022
Some group actions and Fibonacci numbers
Öz: The Fibonacci sequence has many interesting properties and studied by many mathematicians. The terms of this sequence appear in nature and is connected with combinatorics and other branches of mathematics. In this paper, we investigate the orbit of a special subgroup of the modular group. TakingTc:=(c2+c+1−cc21−c)∈Γ0(c2), c∈Z, c≠0,Tc:=(c2+c+1−cc21−c)∈Γ0(c2), c∈Z, c≠0,we determined the orbit {Trc(∞):r∈N}.{Tcr(∞):r∈N}. Each rational number of this set is the form Pr(c)/Qr(c),Pr(c)/Qr(c), where Pr(c)Pr(c) and Qr(c)Qr(c) are the polynomials in Z[c]Z[c]. It is shown that Pr(1)Pr(1) and Qr(1)Qr(1) the sum of the coefficients of the polynomials Pr(c)Pr(c) and Qr(c)Qr(c) respectively, are the Fibonacci numbers, where $P_{r}(c)=sum limits_{s=0}^{r}(begin{array}{c}2r-s send{array}) c^{2r-2s}+sum limits_{s=1}^{r}(begin{array}{c}2r-s s-1end{array}) c^{2r-2s+1}$andQr(c)=r∑s=1(2r−ss−1)c2r−2s+2Qr(c)=∑s=1r(2r−ss−1)c2r−2s+2
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- [1] De˘ger, A. H., Be¸senk, M., G¨uler, B. O., On suborbital graphs and related continued fractions, ¨ Applied Mathematics and Computation, 218 (2011). DOI:10.1016/j.amc.2011.03.065
- [2] G¨uler, B. O., Be¸senk, M., De˘ger, A. H., Kader, S., Elliptic elements and circuits in suborbital ¨ graphs, Hacet, J. Math Stat., 40(2) (2011), 203-210.
- [3] G¨uler, B. O., K¨or, T., S¸anlı, Z., Solution to some congruence equations via suborbital graphs, ¨ SpringerPlus, 5 (2016), 1327. DOI:10.1186/s40064-016-3016-5
- [4] Jones, G. A., Singerman, D., Wicks, K., The Modular Group and Generalized Farey Graphs, London Math. Soc. Lecture Note Series, CUP, Cambridge, 160, 1991, 316-338.
- [5] Lee, G.Y., Kim, J.S., Cho, S.H., Some combinatorial identities via Fibonacci numbers, Discrete Applied Mathematics, 130(3) (2003), 527-534. DOI:10.1016/S0166-218X(03)00331-7
- [6] Koshy, T. Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, 2001.
- [7] Akba¸s, M., K¨or, T., Kesicio˘glu, Y., Disconnectedness of the subgraph F 3 for the group Γ3 , Journal of Inequalities and Applications, 283 (2013). DOI: 10.1186/1029-242X-2013-283
- [8] Keskin, R. Suborbital graphs for the normalizer of Γ0(m), European Journal of Combinatorics, 27 (2006), 193-206. DOI:10.1016/j.ejc.2004.09.004
- [9] Keskin, R., Demirt¨urk, B., On suborbital graphs for the normalizer of Γ0(n), Electron. J. of Combin., 16(1) (2009), 116-133.
- [10] Falc´on, S., Plaza, A., The k-Fibonacci sequence and Pascal 2-triangle, ´ Chaos, Solitons and Fractals, 33(1) (2007), 38-49. DOI: 10.1016/j.chaos.2006.10.022
- [11] Kader, S., G¨uler, B. O., On suborbital graphs for extended modular group ¨ Γ, ˆ Graphs and Combinatorics, 29 (2013), 1813–1825. DOI:10.1007/s00373-012-1226-3
- [12] K¨oro˘glu, T., G¨uler B. O., S¸anlı, Z., Suborbital graphs for the Atkin Lehner group, ¨ Turk. J. of Math., 41 (2017), 235–243. DOI:10.3906/mat-1602-10
| APA | Şanlı z (2022). Some group actions and Fibonacci numbers. , 273 - 284. 10.31801/cfsuasmas.939096 |
| Chicago | Şanlı zeynep Some group actions and Fibonacci numbers. (2022): 273 - 284. 10.31801/cfsuasmas.939096 |
| MLA | Şanlı zeynep Some group actions and Fibonacci numbers. , 2022, ss.273 - 284. 10.31801/cfsuasmas.939096 |
| AMA | Şanlı z Some group actions and Fibonacci numbers. . 2022; 273 - 284. 10.31801/cfsuasmas.939096 |
| Vancouver | Şanlı z Some group actions and Fibonacci numbers. . 2022; 273 - 284. 10.31801/cfsuasmas.939096 |
| IEEE | Şanlı z "Some group actions and Fibonacci numbers." , ss.273 - 284, 2022. 10.31801/cfsuasmas.939096 |
| ISNAD | Şanlı, zeynep. "Some group actions and Fibonacci numbers". (2022), 273-284. https://doi.org/10.31801/cfsuasmas.939096 |
| APA | Şanlı z (2022). Some group actions and Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71(1), 273 - 284. 10.31801/cfsuasmas.939096 |
| Chicago | Şanlı zeynep Some group actions and Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71, no.1 (2022): 273 - 284. 10.31801/cfsuasmas.939096 |
| MLA | Şanlı zeynep Some group actions and Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.71, no.1, 2022, ss.273 - 284. 10.31801/cfsuasmas.939096 |
| AMA | Şanlı z Some group actions and Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(1): 273 - 284. 10.31801/cfsuasmas.939096 |
| Vancouver | Şanlı z Some group actions and Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(1): 273 - 284. 10.31801/cfsuasmas.939096 |
| IEEE | Şanlı z "Some group actions and Fibonacci numbers." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71, ss.273 - 284, 2022. 10.31801/cfsuasmas.939096 |
| ISNAD | Şanlı, zeynep. "Some group actions and Fibonacci numbers". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71/1 (2022), 273-284. https://doi.org/10.31801/cfsuasmas.939096 |
