Peter J. Dukes

collaborators

2 papers

math.CO2026

The deviation from right angles in $k$ -subsets of points in the plane

Peter J. Dukes

A problem originating with Erdős and Silverman in the 1970s asks for the minimum integer $r (k)$ such that any set of $n \geq r (k)$ points in the plane has some $k$ -subset with no ri…

math.CO2025

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids

Will Dolphin, Peter J. Dukes

We improve the status of the problem of determining minimum-sized percolating sets in $a \times b \times c$ grids under the $3$ -neighbour process. Using several new constructions,…

The deviation from right angles in k-subsets of points in the plane

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids

The deviation from right angles in $k$ -subsets of points in the plane