A wide class of Combinatorial matrices related with Reciprocal Pascal and Super Catalan matrices

  • Emrah Kilic TOBB ETU
  • Helmut Prodinger University of Stellenbosch
Keywords: LU-decomposition, Inverse matrix, Zeilberger's algorithm


In this paper, we present a number of combinatorial matrices that are generalizations or variants of the super Catalan matrix and the reciprocal Pascal matrix. We present explicit formulæ for LU-decompositions of all the matrices and their inverses. To prove the claimed results, we mainly use the celebrated Zeilberger algorithm.


I. M. Gessel, Super ballot numbers. J. Symbolic Computation, 14:179{194, 1992.

S. Heubach, N. Y. Li and T. Mansour, A garden of k-Catalan structures. preprint, 2014.

R. Israel, Re: Matrix related to Pascal triangle, sci.math.research, April 2001.

E. Kılıç, I. Akkus, G. Kızılaslan, A variant of the reciprocal super Catalan matrix, Special Matrices 3 (1) (2015), DOI: 10.1515/spma-2015-0014.

E. Kılıç, N. Ömür, S. Koparal, Y. Ulutaş. Two variants of the reciprocal Super Catalan matrix, accepted in Kyungpook J. Math.

E. Kılıç and T. Arıkan, The generalized reciprocal super Catalan matrix, accepted in Turkish J. Math.

H. Prodinger, Factorizations related to the reciprocal Pascal matrix, accepted in Turkish J. Math.

H. Prodinger, The reciprocal super Catalan matrix, Special Matrices 3 (1) 2015, 111-117. DOI: 10.1515/spma-2015-0010.

T. M. Richardson, The reciprocal Pascal matrix. math.CO:arXiv:1405.6315, 2014.

T. M. Richardson, The super Patalan numbers, J. Integer Sequences, Vol. 18 (2015), Article 15.3.3