A variant of the reciprocal super Catalan matrix

Emrah Kılıç; Ilker Akkus; Gonca Kızılaslan

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 163-168, electronic only
  • ISSN: 2300-7451

Abstract

top
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.

How to cite

top

Emrah Kılıç, Ilker Akkus, and Gonca Kızılaslan. "A variant of the reciprocal super Catalan matrix." Special Matrices 3.1 (2015): 163-168, electronic only. <http://eudml.org/doc/271768>.

@article{EmrahKılıç2015,
abstract = {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.},
author = {Emrah Kılıç, Ilker Akkus, Gonca Kızılaslan},
journal = {Special Matrices},
keywords = {Super Catalan numbers; LU-decomposition; Cholesky decomposition; q-analogues; super Catalan numbers; -decomposition; -analogues},
language = {eng},
number = {1},
pages = {163-168, electronic only},
title = {A variant of the reciprocal super Catalan matrix},
url = {http://eudml.org/doc/271768},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Emrah Kılıç
AU - Ilker Akkus
AU - Gonca Kızılaslan
TI - A variant of the reciprocal super Catalan matrix
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 163
EP - 168, electronic only
AB - 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.
LA - eng
KW - Super Catalan numbers; LU-decomposition; Cholesky decomposition; q-analogues; super Catalan numbers; -decomposition; -analogues
UR - http://eudml.org/doc/271768
ER -

References

top
  1. [1] J. E. Andersen and C. Berg, Quantum Hilbert matrices and orthogonal polynomials, math.CA:arXiv:math/0703546v1. Zbl1183.33034
  2. [2] M. D. Choi, Tricks or treats with the Hilbert matrix, Amer. Math. Monthly 90 (5) (1983), 301–312. Zbl0546.47007
  3. [3] D. Hilbert, Ein Beitrag zur Theorie des Legendreschen Polynoms, Acta Math. 18 (1894), 155–159. (367–370 in “Gesammelte Abhandlungen II”, Berlin 1933.) [Crossref] 
  4. [4] E. Kılıç and H. Prodinger, The q-Pilbert matrix, Inter. J. Computer Math., 89 (10) (2012), 1370–1377. Zbl1290.11026
  5. [5] E. Kılıç and H. Prodinger, Variants of the Filbert matrix, The Fibonacci Quarterly 51(2) (2013), 153–162. Zbl1306.11019
  6. [6] V. Y. Pan, Structured matrices and polynomials, Birkhauser Boston, Inc., Boston, MA, Springer-Verlag, New York, 2001. 
  7. [7] M. Petkovsek, H. Wilf, and D. Zeilberger, A = B, A.K. Peters, Ltd., 1996. 
  8. [8] H. Prodinger, The reciprocal super Catalan matrix, Special Matrices 3 (2015), 111–117 Zbl1321.15027
  9. [9] T. M. Richardson, The Filbert matrix, The Fibonacci Quarterly 39 (3) (2001), 268–275. Zbl0994.11011
  10. [10] T. M. Richardson. The reciprocal Pascal matrix, ArXiv:1405.6315, 2014. 
  11. [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. [12] A. Riese, http://www.risc.uni-linz.ac.at/research/combinat/software/qZeil/index.php. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.