An (n, d) permutation array (PA) is a subset of Sn with the property that the distance (under some metric) between any two permutations in the array is at least d. They became popular recently for communication over power lines. Motivated by an application to flash memories, in this paper the metric used is the Chebyshev metric. A number of different constructions are given as well as bounds on the size of such PA.

We study some pumping properties and the classes of languages having these properties. We describe how these classes are interrelated and related to the Chomsky hierarchy of languages. We further study their closure properties.