A4 Refereed article in a conference publication
k-Abelian Equivalence and Rationality
Authors: Julien Cassaigne, Karhumäki Juhani, Puzynina Svetlana, Whiteland Markus
Editors: S. Brlek and C. Reutenauer
Conference name: International Conference on Developments in Language Theory
Publishing place: Berlin
Publication year: 2016
Book title : Developments in Language Theory, 20th International Conference, DLT 2016
Series title: Lecture Notes in Computer Science
Volume: 9840
First page : 77
Last page: 88
Number of pages: 12
ISBN: 978-3-662-53131-0
eISBN: 978-3-662-53132-7
ISSN: 0302-9743
DOI: https://doi.org/10.1007/978-3-662-53132-7_7(external)
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 $v$. We study
some combinatorial properties of $k$-abelian equivalence classes. Our starting point is a
characterization of $k$-abelian equivalence by rewriting, so-called $k$-switching. We show that
the set of lexicographically least representatives of equivalence classes is a regular language.
From this we infer that the sequence of the numbers of equivalence classes is $N$-rational. We
also show that the set of words defining $k$-abelian singleton classes is regular.
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