A variant of the reciprocal super Catalan matrix

• Autorzy: Emrah Kılıç , Ilker Akkus , Gonca Kızılaslan
• Języki publikacji: EN

Abstrakty

EN

Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formulæ for its LU-decomposition, LUdecomposition of its inverse and the Cholesky decomposition are obtained. For all results, q-analogues are also presented.

Słowa kluczowe

EN

Super Catalan numbers; LU-decomposition; Cholesky decomposition; q-analogues

Kategorie tematyczne

• 05A05: Permutations, words, matrices
• 15B05: Toeplitz, Cauchy, and related matrices

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-06-23

zaakceptowano

2015-07-12

online

2015-07-27

Twórcy

autor

Emrah Kılıç

• TOBB University of Economics and Technology, Mathematics Department, 06560 Ankara Turkey

autor

Ilker Akkus

• Kırıkkale University, Faculty of Science and Arts, Department of Mathematics, 71450 Kırıkkale Turkey

autor

Gonca Kızılaslan

• Kırıkkale University, Faculty of Science and Arts, Department of Mathematics, 71450 Kırıkkale Turkey

Bibliografia

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• [4] E. Kılıç and H. Prodinger, The q-Pilbert matrix, Inter. J. Computer Math., 89 (10) (2012), 1370–1377.
• [5] E. Kılıç and H. Prodinger, Variants of the Filbert matrix, The Fibonacci Quarterly 51(2) (2013), 153–162.
• [6] V. Y. Pan, Structured matrices and polynomials, Birkhauser Boston, Inc., Boston, MA, Springer-Verlag, New York, 2001.
• [7] M. Petkovsek, H. Wilf, and D. Zeilberger, A = B, A.K. Peters, Ltd., 1996.
• [8] H. Prodinger, The reciprocal super Catalan matrix, Special Matrices 3 (2015), 111–117
• [9] T. M. Richardson, The Filbert matrix, The Fibonacci Quarterly 39 (3) (2001), 268–275.
• [10] T. M. Richardson. The reciprocal Pascal matrix, ArXiv:1405.6315, 2014.
• [11] A. Riese, A Mathematica q-analogue of Zeilberger’s algorithm for proving q-hypergeometric identities, Diploma Thesis, RISC, J. Kepler University, Linz, Austria, 1995.
• [12] A. Riese, http://www.risc.uni-linz.ac.at/research/combinat/software/qZeil/index.php.

Identyfikatory

DOI

10.1515/spma-2015-0014