A Generalization of the Digital Binomial Theorem

TL;DR

This paper generalizes the digital binomial theorem using Sierpinski matrices, introduces new formulas for Prouhet-Thue-Morse polynomials, and explores algebraic relations among related matrices.

Contribution

It presents a novel one-parameter subgroup of generalized Sierpinski matrices and derives new coefficient formulas and group relations, extending the digital binomial theorem.

Findings

Established a one-parameter subgroup of matrices

Derived new formulas for Prouhet-Thue-Morse coefficients

Described algebraic relations among generating matrices

Abstract

We prove a generalization of the digital binomial theorem by constructing a one-parameter subgroup of generalized Sierpinski matrices. In addition, we derive new formulas for the coefficients of Prouhet-Thue-Morse polynomials and describe group relations satisfied by generating matrices defined in terms of these Sierpinski matrices.