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 = X2 1X 2 2X 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)
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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