Efficient generation of restricted growth words

Abstract

A length n restricted growth word is a word w=w1w2…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.