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- Jarkko Peltomäki, Markus A. Whiteland
- WORDS
- 2015

- Jarkko Peltomäki, Markus A. Whiteland
- Electr. J. Comb.
- 2017

We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope α, there exists exactly six minimal squares in its language (a minimal square does not have a square as a proper prefix). A Sturmian word s of slope α can be written as a product of these six minimal squares: s = X2 1X 2 2X 2 3 · · · . The square root… (More)

- Juhani Karhumäki, Svetlana Puzynina, Michaël Rao, Markus A. Whiteland
- Theor. Comput. Sci.
- 2017

Two words u and v are k-abelian equivalent if for each word x of length at most k, x occurs equally many times as a factor in both u and v. The notion of k-abelian equivalence is an intermediate notion between the abelian equivalence and the equality of words. In this paper, we study the equivalence classes induced by the k-abelian equivalence, mainly… (More)

- Jarkko Peltomäki, Markus A. Whiteland
- WORDS
- 2017

- Julien Cassaigne, Juhani Karhumäki, Svetlana Puzynina, Markus A. Whiteland
- Fundam. Inform.
- 2016

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… (More)

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