#### Some group actions and Fibonacci numbers

Yıl: 2022 Cilt: 71 Sayı: 1 Sayfa Aralığı: 273 - 284 Metin Dili: İngilizce 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
Anahtar Kelime: Suborbital graphs Fibonacci numbers Pascal triangle

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 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