Pascal triangle, Hoggatt matrices, and analogous constructions

TL;DR

This paper explores properties of Hoggatt matrices, their generalizations of Pascal's triangle, and extends the study to q-analogs and Fibonacci analogs, deriving a unified framework.

Contribution

It introduces a common generalization of Hoggatt matrices, q-analogs, and Fibonacci analogs, expanding the understanding of these mathematical structures.

Findings

Hoggatt matrices generalize Pascal's triangle

Derived q-analogs and Fibonacci analogs

Established a unified generalization framework

Abstract

We give an overview about some elementary properties of Hoggatt matrices, which are generalizations of Pascal triangle, and study q-analogs and Fibonacci analogs and derive a common generalization.