@ -276,7 +276,7 @@ Attempt the above construction a few times. Is $w$ a minimal Sturmian word?
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\theorem{}<sturmanthm>
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We can construct a miminal Sturmian word of order $n \geq 3$ as follows:
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We can construct a minimal Sturmian word of order $n \geq 3$ as follows:
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\begin{itemize}
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\item Start with $G_2$, create $R_2$ by removing one edge.
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\item Construct $\mathcal{L}(G_2)$, remove an edge if necessary. \par
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@ -315,7 +315,7 @@ Construct a minimal Sturmain word of order 4.
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$R_4 = \mathcal{L}(R_3)$ is then as shown below, producing the
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order $4$ minimal Sturman word \texttt{11110000}. Disconnected
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nodes are ommited.
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nodes are omitted.
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\begin{center}
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\begin{tikzpicture}
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@ -345,7 +345,7 @@ Construct a minimal Sturmain word of order 5.
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\begin{solution}
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Use $R_4$ from \ref{sturmianfour} to construct $R_5$, shown below. \par
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Disconnected nodes are ommited.
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Disconnected nodes are omitted.
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\begin{center}
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\begin{tikzpicture}
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@ -375,7 +375,7 @@ Construct a minimal Sturmain word of order 5.
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\problem{}
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Argue that the words we get by \ref{sturmanthm} are mimimal Sturmain words. \par
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Argue that the words we get by \ref{sturmanthm} are minimal Sturmain words. \par
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That is, the word $w$ has length $2n$ and $\mathcal{S}_m(w) = m + 1$ for all $m \leq n$.
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\begin{solution}
|
||||
|
Reference in New Issue
Block a user