Let F be a field. We describe Gröbner bases for the ideals of polynomials vanishing on the sets Xn and Ym. Here Xn = X(α1, . . . , αn) is the set of all permutations of some α1, . . . , αn ∈ F. Ym is the set of characteristic vectors of the oriented trees on an m-element vertex set.
