A Digital Binomial Theorem for Sheffer Sequences

2015/10/29 by Toufik Mansour, Mansour, Toufik, Hiêú D. Nguyêñ +1 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Cellular Automata and Applications #Digital Image Processing Techniques #FOS: Mathematics #Number Theory (math.NT) #Primary 11B65 #Secondary 28A80

paper · pdf · doi:10.48550/arxiv.1510.08529

openalex publication_date 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the digital binomial theorem to Sheffer polynomial sequences by demonstrating that their corresponding Sierpiński matrices satisfy a multiplication property that is equivalent to the convolution identity for Sheffer sequences.

Citations

• Sierpinski's triangle and the Prouhet-Thue-Morse word

Cited by

• Generalized Riordan arrays and zero generalized Pascal matrices

Related

• A Digital Binomial Theorem
• A simpler characterization of Sheffer polynomial
• A Generalization of the Digital Binomial Theorem
• On combinatorial properties and the zero distribution of certain Sheffer sequences
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