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 \({\Phi _{{\pi _{1,}}{\pi _2}}}\) 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 {πp, πq} to have property (C) is given, where π is the permutation defined by π(i) = i + 1 mod n and 1 ≤ p < q ≤ n.
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This work was partially supported by National Natural Science Foundation of China (11671294).
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Hou, J., Zhao, H. Positive Maps Constructed from Permutation Pairs. Acta Math Sci 39, 148–164 (2019). https://doi.org/10.1007/s10473-019-0113-x
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DOI: https://doi.org/10.1007/s10473-019-0113-x