Discrete Mathematics and Combinatorics Commons^™

Generalizations Of Pascal's Triangle: A Construction Based Approach, Michael Anton Kuhlmann

UNLV Theses, Dissertations, Professional Papers, and Capstones

The study of this paper is based on current generalizations of Pascal's Triangle, both the expansion of the polynomial of one variable and the multivariate case. Our goal is to establish relationships between these generalizations, and to use the properties of the generalizations to create a new type of generalization for the multivariate case that can be represented in the third dimension.

In the first part of this paper we look at Pascal's original Triangle with properties and classical applications. We then look at contemporary extensions of the triangle to coefficient arrays for polynomials of two forms. The first of …