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)
Extended abstract It is of interest to somehow measure the complexity of an infinite word. One method is to associate the complexity with the complexity of its finite factors. The factor complexity function, P w : N → N, of an infinite word w ∈ Σ N counts, for each n ∈ N, the number of distinct factors of w of length n. The notion has turned out to be a(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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