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.
@article{bwmeta1.element.doi-10_1515_spma-2015-0010, author = {Helmut Prodinger}, title = {The reciprocal super Catalan matrix}, journal = {Special Matrices}, volume = {3}, year = {2015}, zbl = {1321.15027}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0010} }
Helmut Prodinger. The reciprocal super Catalan matrix. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0010/
[1] Emily Allen and Irina Gheorghiciuc, A weighted interpretation for the super catalan numbers, arXiv:1403.5246v2 [math.CO], 2014. | Zbl 1309.05017
[2] Man Duen Choi, Tricks or treats with the Hilbert matrix, Amer. Math. Monthly 90 (1983), no.5, 301–312. | Zbl 0546.47007
[3] I. M. Gessel, Super ballot numbers, J. Symbolic Computation 14 (1992), 179–194. [Crossref] | Zbl 0754.05002
[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] Emrah Kiliç and Helmut Prodinger, Variants of the Filbert matrix, Fibonacci Quart. 51 (2013), no.2, 153–162.
[6] Victor Y. Pan, Structured matrices and polynomials, Birkhäuser Boston, Inc., Boston, MA; Springer-Verlag, New York, 2001.
[7] M. Petkovšek, H. Wilf, and D. Zeilberger, A = B, A.K. Peters, Ltd., 1996.
[8] N. Pippenger and K. Schleich, Topological characteristics of random triangulated surfaces, Random Structures Algorithms 28 (2006), 247–288. | Zbl 1145.52009
[9] T. M. Richardson, The reciprocal Pascal matrix, math.CO:arXiv:1405.6315, 2014.
[10] Thomas M. Richardson, The Filbert matrix, Fibonacci Quart. 39 (2001), no.3, 268-275. | Zbl 0994.11011
[11] Gilles Schaeffer, A combinatorial interpretation of super-Catalan numbers of order two, http://www.lix.polytechnique.fr/ ~schaeffe/Biblio/Slides/SLC54.pdf.