George Beck

collaborators

2 papers

math.CO2021

Reciprocity between partitions and compositions

George Beck, Shane Chern

In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that bot…

math.CO2021

A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence

George Beck, Karl Dilcher

The Stern polynomials defined by $s (0; x) = 0$ , $s (1; x) = 1$ , and for $n \geq 1$ by $s (2 n; x) = s (n; x^{2})$ and $s (2 n + 1; x) = x s (n; x^{2}) + s (n + 1; x^{2})$ have only 0 and 1 as coefficients. We constr…