On the existence of retransmission permutation arrays

We investigate retransmission permutation arrays (RPAs) that are motivated by applications in overlapping channel transmissions. An RPA is an n×nn×n array in which each row is a permutation of {1,…,n}{1,…,n}, and for 1⩽i⩽n1⩽i⩽n, all nn symbols occur in each i×⌈ni⌉ rectangle in specified corners of the array. The array has types 1, 2, 3 and 4 if the stated property holds in the top left, top right, bottom left and bottom right corners, respectively. It is called latin if it is a latin square. We show that for all positive integers nn, there exists a type-1, 2, 3, 4 RPA(n) and a type-1, 2 latin RPA(n).