Monochromatic boxes in colored grids

Joshua Cooper, Stephen Fenner, Semmy Purewal

A $d$-dimensional grid is a set of the form $R=[a_1]\times ...\times [a_d]$. A $d$-dimensional box is a set of the form $\{b_1,c_1\}\times ...\times \{b_d,c_d\}$. When a grid…