Reconstruction of permutations distorted by single reversal errors

The set of permutations on n elements with the metric which is equal to the minimum number of errors being inversions of an interval that transforms one a permutation to other one is investigated. In the paper the problem of finding the minimum number of permutations in a metric ball of a given radius r sufficient to determine uniquely the center of this ball is considered. It is proved that for any n ≥3 this minimum number equals 4 for r = 1 and a simple reconstruction algorithm is given.