symmetric polynomials are the invariants of the classical action of the symmetric group sn on the space q[xn] of polynomials by permutation of the variables. it is well known that the dimension of the quotient of q[xn] by the ideal generated by symmetric, constant-free polynomials is n!. when we consider other actions or other groups, we have different spaces of invariants, and different quotients (coinvariants). we will discuss some examples, in particular quasi-symmetrizing actions, whose coinvariants have dimensions given by the catalan numbers. we shall give explicit grobner bases for the ideals generated by the invariants .