Consecutive Power Occurrences in Sturmian Words
CoRR(2024)
摘要
We show that every Sturmian word has the property that the distance between
consecutive ending positions of cubes occurring in the word is always bounded
by 10 and this bound is optimal, extending a result of Rampersad, who proved
that the bound 9 holds for the Fibonacci word. We then give a general result
showing that for every e ∈ [1,(5+√(5))/2) there is a natural number
N, depending only on e, such that every Sturmian word has the property that
the distance between consecutive ending positions of e-powers occurring in
the word is uniformly bounded by N.
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