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The Gaussian Sequence 3th Order Mod m

Yıl 2024, Cilt: 7 Sayı: 3, 135 - 146, 29.09.2024
https://doi.org/10.33434/cams.1499700

Öz

The work addresses the study of third-order recurrent sequences for mod m cases. Thus, some definitions aim to transform infinite sequences into finite ones. In this regard, the Fourier transform is used as a visualization technique, explored in Google Colab. The mathematical theorems presented are established to examine the patterns of these sequences and their corresponding cycles. As a future perspective, it is intended to investigate other mathematical theorems to generalize the sequences into finite groups.

Kaynakça

  • [1] H. Aydin, R. Dikici, General Fibonacci sequences in finite groups, Fibonacci Quart., 36(3) (1998), 216-221.
  • [2] B. Kuloglu, E. Ozkan, M. Marin, On the period of Pell-Narayana sequence in some groups, arxiv, (2023), 1-16.
  • [3] E. Özkan, 3-step Fibonacci sequences in Nilpotent groups, Appl. Math. Comput., 144(2) (2003), 517-527.
  • [4] E. Özkan, On general Fibonacci sequences in groups, Turkish J. Math., 27(4) (2003) 525-538.
  • [5] D. Wall, Fibonacci series modulo m, The American Mathematical Monthly, 67(6) (1960), 525-532.
  • [6] R. Vieira, E. Spreafico, F. Alves, P. Catarino, A note of the combinatorial interpretation of the Perrin and Tetrarrin sequence, J. Univers. Math., 7(1) (2024), 1-11.
  • [7] R. Vieira, F. Alves, P. Catarino, A note on Leonardo’s combinatorial approach, J. of Instr. Math., 4(2) (2023), 119-126.
  • [8] R. Vieira, F. Alves, P. Catarino, A didactic engineering for the study of the Padovan’s combinatory model, Pedagogical Research, 9(3) (2024), 1-9.
  • [9] F. Alves, Uma discuss˜ao de Artigos envolvendo propriedades da sequencia de Fibonacci apoiada na tecnologia, Anais Do VI HTEM, (2013), 1-17.
  • [10] P. Seenukul, S. Netmanee, T. Panyakhun, R. Auiseekaen, Sa-Muangchan, Matrices which have similar properties to Padovan Q-matrix and its generalized relations, Sakon Nakhon Rajabhat Univ. J. Sci. Tech., 7(2) (2015), 90-94.
  • [11] R. Vieira, F. Alves, Explorando a sequencia de Padovan atraves de investigaao historica e abordagem epistemologica, Boletim GEPEM, 74 (2019), 162-169.
  • [12] A. Shannon, P. Anderson, A. Horadam, Properties of cordonnier, Perrin and Van der Laan numbers, Internat. J. Math. Ed. Sci. Tech., 37(7) (2006), 825-831.
  • [13] J. Shtayat, A. Al-Kaleeb, The Perrin R-matrix and more properties with an application, J. Discrete Math. Sci. Cryptogr., 25(4) (2022), 41-52.
  • [14] J. Ramirez, V. Sirvent, A note on the k-Narayana sequence, Ann. Math. Inform., 45 (2015), 91-105.
  • [15] Y. Soykan, On generalized Narayana numbers, Int. J. Adv. Appl. Math. Mech, 7(3) (2020), 43-56.
  • [16] P. Catarino, A. Borges, On Leonardo numbers, Int. J. Adv. Appl. Math. Mech., 89(1) (2020), 75-86.
  • [17] A. Shannon, O. Devici, A note on generalized and extended Leonardo sequences, Notes Number Theory Discrete Math., 28(1) (2022), 109-114.
  • [18] S. Hulku, O. Erdag, O. Deveci, Complex-type Narayana sequence and its application, Maejo Int. J. Sci. Technol., 17(2) (2023) 163-176.
  • [19] S. Knox, Fibonacci sequences in finite groups Fibonacci sequences in finite groups, Mathematical Sciences Technical Reports (MSTR), 142 (1990), 1-12.
  • [20] B. Kuloglu, E. Ozkan, A. Shannon, The Narayana sequence in finite groups, Fibonacci Quarterly, 60(5) (2022), 212-221.
  • [21] S. Tas, E. Karaduman, The Padovan sequences in finite groups, Chiang Mai J. Sci., 41(2) (2014), 456-462.
  • [22] F. Alves, R. Vieira, P. Catarino, Visualizing the Newtons fractal from the recurring linear sequence with Google Colab: An example of Brazil X Portugal research, Int. Electron. J. Math. Ed., 15(3) (2020), 1-19.
  • [23] M. Aschbacher, Finite Groups Theory, Cambridge University Press, 2000.
  • [24] D. Collins, Generating Sequences of Finite Groups, Cornell University, 2009.
  • [25] D. Tasci, Gaussian Padovan and Gaussian Pell-Padovan sequences, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 67(2) (2018), 82-88.
  • [26] R. P. M. Vieira, Engenharia Didatica (ED): o caso da Generalizacao eComplexificacao da Sequencia de Padovan ou Cordonnier. 2020. 266f. Programa de Pos-Graduacao em Ensino de Ciencias e Matematica, Instituto Federal de Educacao, Ciencia e Tecnologia do Estado do Cear´a. Mestrado Acadˆemico em Ensino de Ciˆencias e Matem´atica, 2020.
  • [27] O. Devici, E. Karaduman, G. Saglam. The Jacobsthal sequences in finite groups, Bull. Iranian Math. Soc., 42(1), 79-89, 2016.
  • [28] M. Kartal, Gaussian Padovan and Gaussian Perrin numbers and properties of them, Asian-Eur. J. Math., 12(4) (2019), 1-8.
  • [29] J. Jordan, Gaussian Fibonacci and Lucas numbers, The Fibonacci Quarterly, 3 (1965), 315-318.
  • [30] E. Özkan, B. Kuloğlu, On The New Narayana Polynomials, The Gauss Narayana Numbers and their polynomials, Asian-Eur. J. Math., 14(6) (2021), 1-15.
  • [31] Y. Soykan, M. Göcen, S. Çevikel, On matrix sequences of Narayana and Narayana-Lucas numbers, Karaelmas Sci. Engrg. J., 11(1) (2021), 83-90.
  • [32] D. Tasci, On Gaussian Leonardo numbers, Contrib. Math., 7 (2023), 34-40.

The Gaussian Sequence 3th Order Mod m

Yıl 2024, Cilt: 7 Sayı: 3, 135 - 146, 29.09.2024
https://doi.org/10.33434/cams.1499700

Öz

The work addresses the study of third-order recurrent sequences for mod m cases. Thus, some definitions aim to transform infinite sequences into finite ones. In this regard, the Fourier transform is used as a visualization technique, explored in Google Colab. The mathematical theorems presented are established to examine the patterns of these sequences and their corresponding cycles. As a future perspective, it is intended to investigate other mathematical theorems to generalize the sequences into finite groups.

Kaynakça

  • [1] H. Aydin, R. Dikici, General Fibonacci sequences in finite groups, Fibonacci Quart., 36(3) (1998), 216-221.
  • [2] B. Kuloglu, E. Ozkan, M. Marin, On the period of Pell-Narayana sequence in some groups, arxiv, (2023), 1-16.
  • [3] E. Özkan, 3-step Fibonacci sequences in Nilpotent groups, Appl. Math. Comput., 144(2) (2003), 517-527.
  • [4] E. Özkan, On general Fibonacci sequences in groups, Turkish J. Math., 27(4) (2003) 525-538.
  • [5] D. Wall, Fibonacci series modulo m, The American Mathematical Monthly, 67(6) (1960), 525-532.
  • [6] R. Vieira, E. Spreafico, F. Alves, P. Catarino, A note of the combinatorial interpretation of the Perrin and Tetrarrin sequence, J. Univers. Math., 7(1) (2024), 1-11.
  • [7] R. Vieira, F. Alves, P. Catarino, A note on Leonardo’s combinatorial approach, J. of Instr. Math., 4(2) (2023), 119-126.
  • [8] R. Vieira, F. Alves, P. Catarino, A didactic engineering for the study of the Padovan’s combinatory model, Pedagogical Research, 9(3) (2024), 1-9.
  • [9] F. Alves, Uma discuss˜ao de Artigos envolvendo propriedades da sequencia de Fibonacci apoiada na tecnologia, Anais Do VI HTEM, (2013), 1-17.
  • [10] P. Seenukul, S. Netmanee, T. Panyakhun, R. Auiseekaen, Sa-Muangchan, Matrices which have similar properties to Padovan Q-matrix and its generalized relations, Sakon Nakhon Rajabhat Univ. J. Sci. Tech., 7(2) (2015), 90-94.
  • [11] R. Vieira, F. Alves, Explorando a sequencia de Padovan atraves de investigaao historica e abordagem epistemologica, Boletim GEPEM, 74 (2019), 162-169.
  • [12] A. Shannon, P. Anderson, A. Horadam, Properties of cordonnier, Perrin and Van der Laan numbers, Internat. J. Math. Ed. Sci. Tech., 37(7) (2006), 825-831.
  • [13] J. Shtayat, A. Al-Kaleeb, The Perrin R-matrix and more properties with an application, J. Discrete Math. Sci. Cryptogr., 25(4) (2022), 41-52.
  • [14] J. Ramirez, V. Sirvent, A note on the k-Narayana sequence, Ann. Math. Inform., 45 (2015), 91-105.
  • [15] Y. Soykan, On generalized Narayana numbers, Int. J. Adv. Appl. Math. Mech, 7(3) (2020), 43-56.
  • [16] P. Catarino, A. Borges, On Leonardo numbers, Int. J. Adv. Appl. Math. Mech., 89(1) (2020), 75-86.
  • [17] A. Shannon, O. Devici, A note on generalized and extended Leonardo sequences, Notes Number Theory Discrete Math., 28(1) (2022), 109-114.
  • [18] S. Hulku, O. Erdag, O. Deveci, Complex-type Narayana sequence and its application, Maejo Int. J. Sci. Technol., 17(2) (2023) 163-176.
  • [19] S. Knox, Fibonacci sequences in finite groups Fibonacci sequences in finite groups, Mathematical Sciences Technical Reports (MSTR), 142 (1990), 1-12.
  • [20] B. Kuloglu, E. Ozkan, A. Shannon, The Narayana sequence in finite groups, Fibonacci Quarterly, 60(5) (2022), 212-221.
  • [21] S. Tas, E. Karaduman, The Padovan sequences in finite groups, Chiang Mai J. Sci., 41(2) (2014), 456-462.
  • [22] F. Alves, R. Vieira, P. Catarino, Visualizing the Newtons fractal from the recurring linear sequence with Google Colab: An example of Brazil X Portugal research, Int. Electron. J. Math. Ed., 15(3) (2020), 1-19.
  • [23] M. Aschbacher, Finite Groups Theory, Cambridge University Press, 2000.
  • [24] D. Collins, Generating Sequences of Finite Groups, Cornell University, 2009.
  • [25] D. Tasci, Gaussian Padovan and Gaussian Pell-Padovan sequences, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 67(2) (2018), 82-88.
  • [26] R. P. M. Vieira, Engenharia Didatica (ED): o caso da Generalizacao eComplexificacao da Sequencia de Padovan ou Cordonnier. 2020. 266f. Programa de Pos-Graduacao em Ensino de Ciencias e Matematica, Instituto Federal de Educacao, Ciencia e Tecnologia do Estado do Cear´a. Mestrado Acadˆemico em Ensino de Ciˆencias e Matem´atica, 2020.
  • [27] O. Devici, E. Karaduman, G. Saglam. The Jacobsthal sequences in finite groups, Bull. Iranian Math. Soc., 42(1), 79-89, 2016.
  • [28] M. Kartal, Gaussian Padovan and Gaussian Perrin numbers and properties of them, Asian-Eur. J. Math., 12(4) (2019), 1-8.
  • [29] J. Jordan, Gaussian Fibonacci and Lucas numbers, The Fibonacci Quarterly, 3 (1965), 315-318.
  • [30] E. Özkan, B. Kuloğlu, On The New Narayana Polynomials, The Gauss Narayana Numbers and their polynomials, Asian-Eur. J. Math., 14(6) (2021), 1-15.
  • [31] Y. Soykan, M. Göcen, S. Çevikel, On matrix sequences of Narayana and Narayana-Lucas numbers, Karaelmas Sci. Engrg. J., 11(1) (2021), 83-90.
  • [32] D. Tasci, On Gaussian Leonardo numbers, Contrib. Math., 7 (2023), 34-40.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Renata Vieira 0000-0002-1966-7097

Renata Teófilo De Sousa 0000-0001-5507-2691

Francisco Regis Alves 0000-0003-3710-1561

Erken Görünüm Tarihi 8 Eylül 2024
Yayımlanma Tarihi 29 Eylül 2024
Gönderilme Tarihi 11 Haziran 2024
Kabul Tarihi 20 Ağustos 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 7 Sayı: 3

Kaynak Göster

APA Vieira, R., Teófilo De Sousa, R., & Alves, F. R. (2024). The Gaussian Sequence 3th Order Mod m. Communications in Advanced Mathematical Sciences, 7(3), 135-146. https://doi.org/10.33434/cams.1499700
AMA Vieira R, Teófilo De Sousa R, Alves FR. The Gaussian Sequence 3th Order Mod m. Communications in Advanced Mathematical Sciences. Eylül 2024;7(3):135-146. doi:10.33434/cams.1499700
Chicago Vieira, Renata, Renata Teófilo De Sousa, ve Francisco Regis Alves. “The Gaussian Sequence 3th Order Mod M”. Communications in Advanced Mathematical Sciences 7, sy. 3 (Eylül 2024): 135-46. https://doi.org/10.33434/cams.1499700.
EndNote Vieira R, Teófilo De Sousa R, Alves FR (01 Eylül 2024) The Gaussian Sequence 3th Order Mod m. Communications in Advanced Mathematical Sciences 7 3 135–146.
IEEE R. Vieira, R. Teófilo De Sousa, ve F. R. Alves, “The Gaussian Sequence 3th Order Mod m”, Communications in Advanced Mathematical Sciences, c. 7, sy. 3, ss. 135–146, 2024, doi: 10.33434/cams.1499700.
ISNAD Vieira, Renata vd. “The Gaussian Sequence 3th Order Mod M”. Communications in Advanced Mathematical Sciences 7/3 (Eylül 2024), 135-146. https://doi.org/10.33434/cams.1499700.
JAMA Vieira R, Teófilo De Sousa R, Alves FR. The Gaussian Sequence 3th Order Mod m. Communications in Advanced Mathematical Sciences. 2024;7:135–146.
MLA Vieira, Renata vd. “The Gaussian Sequence 3th Order Mod M”. Communications in Advanced Mathematical Sciences, c. 7, sy. 3, 2024, ss. 135-46, doi:10.33434/cams.1499700.
Vancouver Vieira R, Teófilo De Sousa R, Alves FR. The Gaussian Sequence 3th Order Mod m. Communications in Advanced Mathematical Sciences. 2024;7(3):135-46.

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