The Reciprocal Pascal Matrix
Thomas M. Richardson
TL;DR
This paper proves that the inverse of the reciprocal Pascal matrix has integer entries, using factorizations of the super Catalan number matrix, revealing new algebraic properties of these matrices.
Contribution
It demonstrates that the inverse of the reciprocal Pascal matrix contains only integers, a novel property proven through factorizations involving super Catalan numbers.
Findings
Inverse of reciprocal Pascal matrix has integer elements
Uses factorizations of super Catalan number matrix
Provides new insights into matrix algebra properties
Abstract
The reciprocal Pascal matrix is the Hadamard inverse of the symmetric Pascal matrix. We show that the ordinary matrix inverse of the reciprocal Pascal matrix has integer elements. The proof uses two factorizations of the matrix of super Catalan numbers.
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Taxonomy
TopicsPolynomial and algebraic computation · Numerical Methods and Algorithms · Modeling and Simulation Systems