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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries

Emrah Kılıç
Neşe Ömür
Sibel Koparal
Sayfa
684–694
Yayın Tarihi
2022-10-18
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers.
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Temel Bulgular & Veri:We shall derive explicit formulae for their $LU$-decompositions and inverses.
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Sonuç & Katkı:To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulae for their $LU$-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.

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Bu Makaleye Atıf Yap

Kılıç, E., Ömür, N., Koparal, S. (2022). New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 684–694. https://ajindex.com/articles/529594

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Kaynakça (22)

  1. C. Berg, Fibonacci numbers and orthogonal polynomials, Arab. J. Math. Sci. 17, 75– 88, 2011
  2. L. Carlitz, Some determinants of q-binomial coefficients, J. Reine Angew. Math. 226, 216–220, 1967
  3. W. Chu, On the evaluation of some determinants with q-binomial coefficients, J. Systems Sci. Math. Science 8 (4), 361–366, 1988
  4. W. Chu, Generalizations of the Cauchy determinant, Publ. Math. Debrecen 58 (3), 353–365, 2001
  5. W. Chu and L. Di Claudio, Binomial determinant evaluations, Ann. Comb. 9 (4), 363–377, 2005
  6. W. Chu, Finite differences and determinant identities, Linear Algebra Appl. 430, 215–228, 2009
  7. M.E.H. Ismail, One parameter generalizations of the Fibonacci and Lucas numbers, The Fibonacci Quart. 46/47, 167–180, 2008/2009
  8. E. Kılıç and H. Prodinger, A generalized Filbert matrix, The Fibonacci Quart. 48, 29–33, 2010
  9. E. Kılıç and H. Prodinger, The q-Pilbert matrix, Int. J. Comput. Math. 89, 1370– 1377, 2012
  10. E. Kılıç and H. Prodinger, Variants of the Filbert matrix, The Fibonacci Quart. 51, 153–162, 2013
  11. E. Kılıç and H. Prodinger, Asymmetric generalizations of the Filbert matrix and variants, Publ. Inst. Math. (Belgrad) (N.S) 95 (109), 267–280, 2014
  12. E. Kılıç and H. Prodinger, The generalized q-Pilbert matrix, Math. Slovaca 64, 1083– 1092, 2014
  13. E. Kılıç and H. Prodinger, The generalized Lilbert matrix, Periodica Math. Hungar. 73, 62–72, 2016
  14. G.Y. Lee, S.G. Lee, and H.G. Shin, On the k-generalized Fibonacci matrix $Q_{K}^{ast }$, Linear Algebra Appl. 251, 73–88, 1997
  15. G.Y. Lee and S.H. Cho, The generalized Pascal matrix via the generalized Fibonacci matrix and the generalized Pell matrix, J. Korean Math. Soc. 45 (2), 479–491, 2008
  16. M. Merca, A note on the determinant of a Toeplitz-Hessenberg matrix, Spec. Matrices 1, 10–16, 2013
  17. A.M. Ostrowski, On some determinants with combinatorial numbers, J. Reine Angew. Math. 216, 25–30, 1964
  18. M. Petkovsek, H. Wilf, and D. Zeilberger, A=B, A.K. Peters, Wellesley, MA, 1996
  19. H. Prodinger, A generalization of a Filbert matrix with 3 additional parameters, Trans. Roy. Soc. South Afr. 65, 169–172, 2010
  20. T.M. Richardson, The Filbert matrix, The Fibonacci Quart. 39 (3), 268–275, 2001
  21. J. Zhou and J. Zhaolin, The spectral norms of g-circulant matrices with classical Fibonacci and Lucas numbers entries, Appl. Math. Comput. 233, 582–587, 2014
  22. J. Zhou and J. Zhaolin, Spectral norms of circulant-type matrices with binomial co