Criteria of positivity for linear maps constructed from permutation pairs

Haili Zhao, Jinchuan Hou

In this paper, we show that a $D$-type map ${\Phi }_D:M_n\to M_n$ with $D=(n-2)I_n+P_{{\pi }_1}+P_{{\pi }_2}$ induced by a pair $\{{\pi }_1,{\pi }_2\}$ of permutations of $(1,2,...,n)$ is positive…