The reciprocal super Catalan matrix

• Autorzy: Helmut Prodinger
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Super Catalan numbers; LU-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

2015-03-14

zaakceptowano

2015-05-19

online

2015-05-28

Twórcy

autor

Helmut Prodinger

• Kobe Gakuin University, Kobe, 650-8586, Japan

Bibliografia

• [1] Emily Allen and Irina Gheorghiciuc, A weighted interpretation for the super catalan numbers, arXiv:1403.5246v2 [math.CO], 2014.
• [2] Man Duen Choi, Tricks or treats with the Hilbert matrix, Amer. Math. Monthly 90 (1983), no.5, 301–312.
• [3] I. M. Gessel, Super ballot numbers, J. Symbolic Computation 14 (1992), 179–194. [Crossref]
• [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.
• [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.
• [11] Gilles Schaeffer, A combinatorial interpretation of super-Catalan numbers of order two, http://www.lix.polytechnique.fr/ ~schaeffe/Biblio/Slides/SLC54.pdf.

Identyfikatory

DOI

10.1515/spma-2015-0010