3 papers
math.GM2024
Novel required properties of, and efficient algorithms to seek, perfect cuboids
Aubrey de Grey, Philip Gibbs, Louie Helm
We present a novel approach to the age-old question of whether perfect cuboids exist. Our approach consists of two new computer search algorithms, arising from the analysis of "per…
math.CO2023
On lower bounds of the order of -chromatic unit distance graphs
Aubrey D. N. J. de Grey, Jaan Parts
Here we give refined numerical values for the minimum number of vertices of -chromatic unit distance graphs in the Euclidean plane.
math.CO2022
Tiling the plane with hexagons: improved separations for -colourings
Aubrey D. N. J. de Grey, Jaan Parts
It has been common knowledge since 1950 that seven colours can be assigned to tiles of an infinite honeycomb with cells of unit diameter such that no two tiles of the same colour a…