Markus A. Whiteland

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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 = X 2 1 X 2 2 X 2 3 · · ·. The square root(More)
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)
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