Discrepancy of High-Dimensional Permutations

Nathan Linial, Zur Luria

Let $L$ be an order-$n$ Latin square. For $X,Y,Z\subseteq \{1,...,n\}$, let $L(X,Y.Z)$ be the number of triples $i\in X,j\in Y,k\in Z$ such that $L(i,j)=k$. We conjectur…