The Pascal matrix in the multivariate Riordan group

TL;DR

This paper extends Pascal matrices to multidimensional binomial coefficient matrices linked to point sets, demonstrating their membership in the multivariate Riordan group.

Contribution

It introduces a generalization of Pascal matrices using multidimensional binomial coefficients and proves their inclusion in the multivariate Riordan group.

Findings

Matrices associated with integral coordinate point sets are in the multivariate Riordan group.

The paper establishes properties of these generalized Pascal matrices.

It broadens the understanding of Pascal matrices in higher dimensions.

Abstract

We generalize the concept of Pascal matrices to matrices associated with sets of points by considering multidimensional binomial coefficients as entries. We study their properties and prove that the infinite matrix associated with the set vectors with integral coordinates is in fact an element of the multivariate Riordan group.