A Generalization of the Digital Binomial Theorem

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.

14 pages

References in corpus (3)

• A Digital Binomial Theorem
• Sierpinski's triangle and the Prouhet-Thue-Morse word
• A New Proof of the Prouhet-Tarry-Escott Problem