Efficient generation of restricted growth words

A length n restricted growth word is a word w=^{w1 w2}.^wn over the set of integers where ^w1=0 and each ^wi, i>1, lies between 0 and the value of a word statistics of the prefix ^w1w2.wi-₁ of w, plus one. Restricted growth words simultaneously generalize combinatorial objects as restricted growth functions, staircase words and ascent or binary sequences. Here we give a generic generating algorithm for restricted growth words. It produces a Gray code and runs in constant average time provided that the corresponding statistics has some local properties.