For each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha \) (Q1010692)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | For each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha \) |
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For each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha \) (English)
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7 April 2009
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Summary: The critical exponent of an infinite word \({\mathbf w}\) is the supremum of all rational numbers \(\alpha\) such that \({\mathbf w}\) contains an \(\alpha\)-power. We resolve an open question of Krieger and Shallit by showing that for each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha\).
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combinatorics on words
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repetitions
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critical exponent
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