Mutually Abelian-Bordered Binary Words
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916969699082240 |
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| author | Maity, Anuran Krishna, K. V. |
| author_facet | Maity, Anuran Krishna, K. V. |
| contents | A word is said to be bordered if it contains a nonempty proper prefix that is also a suffix. A pair of words $(u, v)$ is said to be mutually bordered if there exists a word that is a nonempty proper prefix of $u$ and suffix of $v$, and there exists a word that is a nonempty proper suffix of $u$ and prefix of $v$. Recently, Gabric studied the number of mutually bordered pairs. In this work, we extend the concept of mutually bordered pairs to abelian setting, and determine the number of mutually abelian-bordered pairs of binary words using lattice paths. We also find the number of unbordered pairs in this context. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_20773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutually Abelian-Bordered Binary Words Maity, Anuran Krishna, K. V. Combinatorics 68R15 A word is said to be bordered if it contains a nonempty proper prefix that is also a suffix. A pair of words $(u, v)$ is said to be mutually bordered if there exists a word that is a nonempty proper prefix of $u$ and suffix of $v$, and there exists a word that is a nonempty proper suffix of $u$ and prefix of $v$. Recently, Gabric studied the number of mutually bordered pairs. In this work, we extend the concept of mutually bordered pairs to abelian setting, and determine the number of mutually abelian-bordered pairs of binary words using lattice paths. We also find the number of unbordered pairs in this context. |
| title | Mutually Abelian-Bordered Binary Words |
| topic | Combinatorics 68R15 |
| url | https://arxiv.org/abs/2509.20773 |