k-Abelian Equivalence and Rationality

Abstract

International audienc

Regularity of k-Abelian Equivalence Classes of Fixed Cardinality

“…Another result, more in the spirit of classical formal language theory, is shown in [2] (for a detailed proof, see [3]):…”

“…This turned out to be quite an interesting approach. It allowed, see [2,3], to show that the union of singleton classes is a regular language. Similarly, the set of all lexicographically least (or, equivalently, greatest) representatives constitutes a regular set.…”

k-Abelian Equivalence and Rationality

“…Finally, using the automata-theoretic characterization of the complexity function, we solve the open problem of the original conference version, by showing that for each m and k the complexity function P k,m giving the number of equivalence classes of words of length n, is not only of order Θ n m k−1 (m−1) , but actually asymptotic to Cn m k−1 (m−1) for some rational constant C. This paper is an extended full version of the conference presentation [11]. Here v = S k,u (i, j, l, m); the white rectangles symbolize x and the black rectangles symbolize y.…”