Gauss Narayana ve Gauss Narayana-Lucas Hibrit sayıları

Öz

Karmaşık, hiperbolik ve dual sayıları genelleştiren hibrit sayılar, bugüne kadar kapsamlı araştırmaların konusu olmuştur. Bu çalışmada, hibrit sayılar teorisini Gauss-Narayana ve Gauss-Narayana-Lucas dizileriyle birleştirerek Gauss-Narayana Hibrit ve Gauss-Narayana-Lucas Hibrit sayılarını tanıtıyoruz. Ayrıca, bu yeni tanımlanan sayıların tekrarlama ilişkileri, Binet tipi formüller ve toplam özdeşlikleri de dahil olmak üzere çeşitli cebirsel özelliklerini sunuyoruz.

Anahtar Kelimeler

• Hibrit sayıları
• Narayana dizisi
• narayana-lucas dizisi

On Gaussianian Narayana and Gaussianian Narayana-Lucas Hybrid Numbers

Öz

Hybrid numbers, which generalize complex, hyperbolic, and dual numbers, have been the subject of extensive research to date. In this study, we introduce the Gaussian–Narayana Hybrid and Gaussian–Narayana–Lucas Hybrid numbers by combining hybrid number theory with the Gaussian Narayana and Gaussian Narayana–Lucas sequences. We also present several algebraic properties of these newly defined numbers, including their recurrence relations, Binet-type formulas, and summation identities.

Anahtar Kelimeler

• Hybrid numbers
• Narayana numbers
• Narayana-Lucas numbers

Kaynakça

1. Berzsenyi, G. (1977), Gaussianian Fibonacci numbers, Fibonacci Quarterly, 15, 233–236.
2. Deniz Tuncay, Bilgici Goksal, Dasdemir Ahmet and Unal Zafer (2020), A study on Horadam Hybrid Numbers, Turkish Journal of Mathematics 44(4), 1212-1221.
3. Didkivska T. V. and St’opochkina M. V. (2003), Properties of Fibonacci-Narayana numbers, In the World of Math. 9(1) 29–36.
4. Er M.C. (1984), Sums of Fibonacci Numbers by Matrix Methods, Fibonacci Quarterly, 22(3) 204-207.
5. Horadam, A. F. (1961), Generalized Fibonacci sequence, American Math. Monthly, 68, 455-459.
6. Horadam A. F. (1993), Quaternion recurrence relations, Ulam Quarterly, 2, 23–33.
7. Karaaslan N., Fazlıoğlu M. (2021), On the Gaussianian Narayana-Lucas Numbers, Aksaray University Journal of Science and Engineering, 5(2),125-137.
8. Kızılateş, C. (2020), A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos Solitons and Fractals, 130, 1-5.

9. Koshy T. (2001), Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, Inc., Canada.
10. Jose L. Ramirez and Victor F. Sirvent (2015), A note on the k-Narayana sequence, Ann. Math. Inf. 45 91–105.
11. Ozdemir M. (2018), Introduction to hybrid numbers, Advances in Applied Clifford Algebras, 28 (1), 11.
12. Ozkan E. and Tastan M. (2019), On Gaussian Fibonacci polynomials, on Gaussian Lucas polynomials and their applications, Communications in Algebra doi:10.1080/00927872.1670193. https://doi.org/10.1080/00927872.2019.1670193.
13. Ozkan E. and Kuloglu B. (2021), On the new Narayana polynomials, the Gaussian Narayana numbers and their polynomials, Asian-European Journal of Mathematics, 14 (6), Paper No. 2150100, 16 pp.
14. Petroudi Seyyed, Pirouz Maryam, and Özkoc Arzu (2021), The Narayana Polynomial and Narayana Hybrinomial Sequences, Konuralp Journal of Mathematics 9(1), 90-99.
15. Ramirez Jose L. and Sirvent Victor F. (2015), A note on the k-Narayana sequence, Ann. Math. Inf., 45, 91–105.
16. Soykan Y. (2020), On Generalized Narayana numbers, International Journal of Advances in Applied Mathematics and Mechanics, 7(3), 43 – 56.
17. Szynal-Liana A., Włoch I. (2019), The Fibonacci hybrid numbers, Utilitas Math., 110, 3-10.
18. Szynal-Liana A. (2018), The Horadam hybrid numbers, Discuss Math. Gen Algebra App., 38, 91-98.