2 problems

High-dimensional permutation discrepancy conjecture. For every $d\geq2$ there exist arbitrarily large $d$-dimensional permutations $A$ such that, for every box $\mathcal T$,

Let $H$ be a graph, let $\Lambda$ be a vector of vertex weights, and let $mgeq 2$ be even. Write $Hom({\mathbb Z}^d_m,H)$ for the set of $H$-colorings of the $m$-ary $d$-dimensional…