On circular disarranged strings of sequences

Two sequences (a1, a2, ... , an) and (b1, b2, ..., bn), sharing n-1 elements, are said disarranged if for every non-empty subset Q of [n], the sets {ai : i in Q} and {bi : i in Q} are different. In this paper we investigate properties of these pairs of sequences. Moreover we extend the definition of disarranged pairs to a circular string of n-sequences and prove that, for every positive integer m, except some initials values for n even, there exists a similar structure of length m.