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

Authors

  • Emrah Kilic TOBB ETU
  • Helmut Prodinger University of Stellenbosch

DOI:

https://doi.org/10.11575/cdm.v14i1.62631

Keywords:

LU-decomposition, Inverse matrix, Zeilberger's algorithm

Abstract

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.

References

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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.

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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

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Published

2019-12-25

Issue

Vol. 14 No. 1 (2019)

Section

Articles

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