8 citations · 25 across the 15 of their papers we have counts for
9 papers · 1 filter
The area of the Mandelbrot set and Zagier's conjecture
Patrick F. Bray, Hieu D. Nguyen
We prove Zagier's conjecture regarding the 2-adic valuation of the coefficients that appear in Ewing and Schober's series formula for the area of the Mandelbrot set in th…
A Digital Binomial Theorem for Sheffer Sequences
Toufik Mansour, Hieu D. Nguyen
We extend the digital binomial theorem to Sheffer polynomial sequences by demonstrating that their corresponding Sierpiński matrices satisfy a multiplication property that is equiv…
A -Digital Binomial Theorem
Toufik Mansour, Hieu D. Nguyen
We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.
A Generalization of the Digital Binomial Theorem
Hieu D. Nguyen
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 c…
A Digital Binomial Theorem
Hieu D. Nguyen
We present a triangle of connections between the Sierpinski triangle, the sum-of-digits function, and the Binomial Theorem via a one-parameter family of Sierpinski matrices, which…
A New Proof of the Prouhet-Tarry-Escott Problem
Hieu D. Nguyen
The famous Prouhet-Tarry-Escott problem seeks collections of mutually disjoint sets of non-negative integers having equal sums of like powers. In this paper we present a new proof…