  We propose a technique for exploring the abelian complexity of recurrent
infinite words, focusing particularly on infinite words associated with Parry
numbers. Using that technique, we give the affirmative answer to the open
question posed by Richomme, Saari and Zamboni, whether the abelian complexity
of the Tribonacci word attains each value in $\{4,5,6\}$ infinitely many times.
