A symmetric function is a function which is unchanged under any permutation of its variables, for example:
$$f(x,y,z) = x^2+y^2+z^2+xy+xz+yz$$
There are sets of functions in which the individual functions are not symmetric but the set as a whole is unchanged under any permutation of the variables in the functions. An example is the set comprising the following three functions:
$$f(x,y,z) = x^2 + yz$$ $$g(x,y,z) = y^2 + xz$$ $$h(x,y,z) = z^2 + xy$$
Is there a term for such a set of functions?