Regularity of k-Abelian equivalence classes of fixed cardinality

Abstract

Two words u and v are said to be k-Abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v. In this note we continue the analysis of k-Abelian equivalence classes. In particular, we show that, for any fixed integer r≥ 1, the language of words representing equivalence classes of cardinality r is regular.