Joel Miller

activity

20222025

collaborators

6 papers

math.CO2025

Matrix Apportionment: General Cases and Apportionment Constants

Dustin R. Baker, Bryan A. Curtis, Joe Miller +1

A matrix is apportionable if it is similar to a matrix whose entries have equal moduli. This paper shows that all nilpotent matrices and all matrices with rank at most half their o…

math.CO2025

Full classification of anti-van der Waerden numbers of graph products of forests

Zhanar Berikkyzy, Joe Miller, Nathan Warnberg

The anti-van der Waerden number of a graph $G$ is the fewest number of colors needed to guarantee a rainbow $3$ -term arithmetic progression in $G$ , denoted $aw (G, 3)$ …

math.CO2024

On the proper rainbow saturation numbers of cliques, paths, and odd cycles

Dustin Baker, Enrique Gomez-Leos, Anastasia Halfpap +7

Given a graph $H$ , we say a graph $G$ is properly rainbow $H$ -saturated if there is a proper edge-coloring of $G$ which contains no rainbow copy of $H$ , but adding any edge to $G$ …

math.CO2023

Anti-van der Waerden Numbers of Graph Products with Trees

Zhanar Berikkyzy, Joe Miller, Elizabeth Sprangel +2

Given a graph $G$ , an exact $r$ -coloring of $G$ is a surjective function $c : V (G) \to [1, \dots, r]$ . An arithmetic progression in $G$ of length $j$ with common difference $d$ is a se…

math.CO2023

Rainbow numbers of $[m] \times [n]$ for $x_{1} + x_{2} = x_{3}$

Kean Fallon, Ethan Manhart, Joe Miller +3

Consider the set $[m] \times [n] = {(i, j) : 1 \leq i \leq m, 1 \leq j \leq n}$ and the equation $x_{1} + x_{2} = x_{3}$ , namely $e q$ . The \emph{rainbow number of $[m] \times [n]$ for $e q$ }, d…

math.CO2022

Anti-van der Waerden Numbers of Graph Products of Cycles

Joe Miller, Nathan Warnberg

A $k$ -term arithmetic progression ( $k$ -AP) in a graph $G$ is a list of vertices such that each consecutive pair of vertices is the same distance apart. If $c$ is a coloring functio…