On the rank of a Latin tensor

An n×n matrix A is called permutative if the rows of A are distinct permutations of a family of n distinct elements. For all n⩾3, we show that the minimal rank of a non-negative permutative matrix equals 3. The minimal rank of a generic permutative n×n matrix equals the smallest integer r such that r!⩾n. Our results answer the questions asked recently by Hu, Johnson, Davis, Zhang, and we show how to generalize them to tensors.