Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.03205 |
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Sommario:
- Enumerating the number of times one word occurs in another is a much-studied combinatorial subject. By utilizing a method that we call ``lexicographic extreme referencing'', we provide a formula for computing occurrences of one binary word in another. We then study $B_{n,p}(k)$, the number of binary words of length $n$ containing a given word $p$ exactly $k$ times. For this purpose, we first use lexicographic extreme referencing to provide an algorithm for constructing all words $w$ that contain a given word $p$. Afterward, we give a modified version of this algorithm for constructing the subset of binary words that are ``primitive'' with respect to $p$, and we discuss approaches for finding $B_{n,p}(k)$ via primitive words.