Generating all permutations by context-free grammars in Greibach normal form

We consider context-free grammars Gn in Greibach normal form and, particularly, in Greibach m-form (m = 1, 2) which generates the finite language Ln of all n! strings that are permutations of n different symbols (n ≥ 1). These grammars are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of Gn as functions of n. As in the case of Chomsky normal form these descriptional complexity measures grow faster than any polynomial function.