Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, the 𝐶𝐿𝑘,𝑛 description of Catalan transformation of 𝑘−Lucas 𝐿𝑘,𝑛 sequences was given.
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Key Findings & Data:And also, 𝐶𝐿𝑘,𝑛 transformation was written as the multiplying of Catalan matris C which is the lower triangular matris, and the 𝐿𝑘 matris of 𝑛 𝑥 1 type.
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Conclusion & Impact:Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:k-Lucas dizisi · k-Fibonacci dizisi · Catalan dönüşümü
Abstract
In this study, the 𝐶𝐿𝑘,𝑛 description of Catalan transformation of 𝑘−Lucas 𝐿𝑘,𝑛 sequences was given. The 𝐶𝐿𝑘,𝑛 generating function of Catalan transformation of 𝑘−Lucas 𝐿𝑘,𝑛 sequences was obtained. And also, 𝐶𝐿𝑘,𝑛 transformation was written as the multiplying of Catalan matris C which is the lower triangular matris, and the 𝐿𝑘 matris of 𝑛 𝑥 1 type. Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.
Özet
Bu çalışmada, k- Lucas dizisinin Catalan dönüşümünün tanımı verildi. k- Lucas dizisinin Catalan dönüşümünün geren fonksiyonu elde edildi. Ayrıca, Hankel fonksiyonu kullanılarak oluşturulan matrislerin determinantları hesaplandı.
Özkan, E., Taştan, M., Güngör, O., *, M. T. (2020). Catalan Transform of The 𝒌−Lucas Numbers. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 Sayı: ÖZEL SAYI I Özel Sayı, 145–149. https://doi.org/10.18185/erzifbed.638488
Barry, P. (2005), A Catalan transform and related transformations on integer sequences. J.Integer Seq., 8(4), 1-24.
Cvetkovi´c, A., Rajkovi´c, R., and Ivkovi´c, M. (2002), Catalan numbers, and Hankel transform, and Fibonacci numbers. J. Integer Seq. 5(1), 1-8.
Özkan, E., Taştan, M., Aydoğdu, A, (2018), 2-Fibonacci Polynomials in the Family of Fibonacci Numbers, Notes on Number Theory and Discrete Mathematics, 24, 47-55.