Abstract
If all proper factors of a word u are β-power-free while u itself is not, then u is a minimal β-power. We consider the following general problem: for which numbers k,β, and p there exists a k-ary minimal β-power of period p? For the case β ≥ 2 we completely solve this problem. If the number β< 2 is relatively ”big” w.r.t. k, we show that any number p can be the period of a minimal β-power. Finally, for ”small” β we describe some sets of forbidden periods and provide a numerical evidence that for k ≥ 9 these sets are almost exhaustive.
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Shur, A.M. (2010). On the Existence of Minimal β-Powers. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_37
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DOI: https://doi.org/10.1007/978-3-642-14455-4_37
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