George Beck

activity

20212026

collaborators

4 papers

math.NT2026

Reciprocals of Subsum Polynomials

Cristina Ballantine, George Beck, Brooke Feigon +1

We introduce the subsum polynomial of a partition $λ = (λ_{1}, λ_{2}, \dots, λ_{k})$ defined by $sp (λ, x) = \prod_{i = 1}^{k} (1 + x^{λ_{i}})$ . We study the sum of reciprocals of $\mathrm{s…

math.CO2023

Partitions enumerated by self-similar sequences

Cristina Ballantine, George Beck

The Fibonacci numbers are the prototypical example of a recursive sequence, but grow too quickly to enumerate sets of integer partitions. The same is true for the other classical s…

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…