Jonathan Joe

collaborators

3 papers

math.CO2024

Problems on the Triangular Lattice

Gaston A. Brouwer, Jonathan Joe, Abby A. Noble +1

In this work, we consider a number of problems defined on the triangular lattice with $n$ rows, which we will denote as $T_{n}$ . Define a \textit{proper coloring} to be an assignment…

math.NT2023

Odd Vector Cycles in $Z^{m}$

Gaston A. Brouwer, Jonathan Joe, Matt Noble

Given positive integers $m$ and $r$ , define $C_{m} (r)$ to be the minimum odd number of $Z^{m}$ vectors, each of magnitude $r$ , that together sum to the zero vector. In…

math.CO2023

A Triangle-free, 4-chromatic $Q^{3}$ Euclidean Distance Graph Scavenger Hunt!

Jonathan Joe, Matt Noble

For $d > 0$ , define $G (Q^{3}, d)$ to be the graph whose set of vertices is the rational space $Q^{3}$ , where two vertices are adjacent if and only if they are a Eucli…

Problems on the Triangular Lattice

Odd Vector Cycles in Zm

A Triangle-free, 4-chromatic Q3 Euclidean Distance Graph Scavenger Hunt!

Odd Vector Cycles in $Z^{m}$

A Triangle-free, 4-chromatic $Q^{3}$ Euclidean Distance Graph Scavenger Hunt!