  Permutation polynomials are of particular significance in several areas of
applied mathematics, such as Coding theory and Cryptography. Many recent
constructions are based on the Akbary-Ghioca-Wang (AGW) criterion. Along this
line of research, we provide new classes of permutation trinomials in
$\mathbb{F}_{q^2}$ of the form $f(x)=x^r h(x^{q-1})$, by studying permutations
of the set of $(q+1)$-th roots of unity, which look like monomials on the sets
of suitable partitions.
