The reciprocal super Catalan matrix

Helmut Prodinger

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 111-117, electronic only
  • ISSN: 2300-7451

Abstract

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The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.

How to cite

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Helmut Prodinger. "The reciprocal super Catalan matrix." Special Matrices 3.1 (2015): 111-117, electronic only. <http://eudml.org/doc/270974>.

@article{HelmutProdinger2015,
abstract = {The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.},
author = {Helmut Prodinger},
journal = {Special Matrices},
keywords = {Super Catalan numbers; LU-decomposition; q-analogues; super Catalan numbers; -analogues; super Catalan matrix},
language = {eng},
number = {1},
pages = {111-117, electronic only},
title = {The reciprocal super Catalan matrix},
url = {http://eudml.org/doc/270974},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Helmut Prodinger
TI - The reciprocal super Catalan matrix
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 111
EP - 117, electronic only
AB - The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
LA - eng
KW - Super Catalan numbers; LU-decomposition; q-analogues; super Catalan numbers; -analogues; super Catalan matrix
UR - http://eudml.org/doc/270974
ER -

References

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  1. [1] Emily Allen and Irina Gheorghiciuc, A weighted interpretation for the super catalan numbers, arXiv:1403.5246v2 [math.CO], 2014. Zbl1309.05017
  2. [2] Man Duen Choi, Tricks or treats with the Hilbert matrix, Amer. Math. Monthly 90 (1983), no.5, 301–312. Zbl0546.47007
  3. [3] I. M. Gessel, Super ballot numbers, J. Symbolic Computation 14 (1992), 179–194. [Crossref] Zbl0754.05002
  4. [4] I. M. Gessel and G. Xin, A combinatorial interpretation of the numbers 6(2n)!/n!(n + 2)!, J. Integer Seq. 8 (2005), Article 05.2.3. 
  5. [5] Emrah Kiliç and Helmut Prodinger, Variants of the Filbert matrix, Fibonacci Quart. 51 (2013), no.2, 153–162. 
  6. [6] Victor Y. Pan, Structured matrices and polynomials, Birkhäuser Boston, Inc., Boston, MA; Springer-Verlag, New York, 2001. 
  7. [7] M. Petkovšek, H. Wilf, and D. Zeilberger, A = B, A.K. Peters, Ltd., 1996. 
  8. [8] N. Pippenger and K. Schleich, Topological characteristics of random triangulated surfaces, Random Structures Algorithms 28 (2006), 247–288. Zbl1145.52009
  9. [9] T. M. Richardson, The reciprocal Pascal matrix, math.CO:arXiv:1405.6315, 2014. 
  10. [10] Thomas M. Richardson, The Filbert matrix, Fibonacci Quart. 39 (2001), no.3, 268-275. Zbl0994.11011
  11. [11] Gilles Schaeffer, A combinatorial interpretation of super-Catalan numbers of order two, http://www.lix.polytechnique.fr/ ~schaeffe/Biblio/Slides/SLC54.pdf. 

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