The Number of Positions Starting a Square in Binary Words

The Number of Positions Starting a Square in Binary Words

We consider the number $\sigma(w)$ of positions that do not start a square in binary words $w$. Letting $\sigma(n)$ denote the maximum of $\sigma(w)$ for length $|w|=n$, we show that $\lim \sigma(n)/n = 15/31$.

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Veröffentlicht in:The Electronic journal of combinatorics 2011-01, Vol.18 (1)
Hauptverfasser: Harju, Tero, Kärki, Tomi, Nowotka, Dirk
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creator Harju, Tero
Kärki, Tomi
Nowotka, Dirk
description We consider the number $\sigma(w)$ of positions that do not start a square in binary words $w$. Letting $\sigma(n)$ denote the maximum of $\sigma(w)$ for length $|w|=n$, we show that $\lim \sigma(n)/n = 15/31$.
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