A variant of the reciprocal super Catalan matrix

Abstract

Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formulæ for its LU-decomposition, LUdecomposition of its inverse and the Cholesky decomposition are obtained. For all results, q-analogues are also presented.

Keywords

• Super Catalan numbers
• LU-decomposition
• Cholesky decomposition
• q-analogues
• 15B05
• 05A05