POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

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