How many square occurrences must a binary sequence contain? (Q1871376)
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scientific article; zbMATH DE number 1907097
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | How many square occurrences must a binary sequence contain? |
scientific article; zbMATH DE number 1907097 |
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How many square occurrences must a binary sequence contain? (English)
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7 May 2003
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Summary: Every binary word with at least four letters contains a square. A. Fraenkel and J. Simpson showed that three distinct squares are necessary and sufficient to construct an infinite binary word. We study the following complementary question: how many square occurrences must a binary word contain? We show that this quantity is, in the limit, a constant fraction of the word length, and prove that this constant is 0.55080....
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