Abstract: A property (C) for permutation pairs is introduced. It is shown that if a pair {π₁, π₂} of permutations of (1, 2, …, n) has property (C), then the D-type map Φ_{π1, π2} on n×n complex matrices constructed from {π₁, π₂} is positive. A necessary and sufficient condition is obtained for a pair {π₁, π₂} to have property (C), and an easily checked necessary and sufficient condition for the pairs of the form {π^p, π^q} to have property (C) is given, where π is the permutation defined by π(i)=i + 1 mod n and 1 ≤ p < q ≤ n.

Key words: matrix algebras, positive linear maps, permutations, quantum information