Words with Repeated Letters in a Grid
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917107366625280 |
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| author | Halberstam, Zachary Schildkraut, Carl |
| author_facet | Halberstam, Zachary Schildkraut, Carl |
| contents | Given a word $w$, what is the maximum possible number of appearances of $w$ reading contiguously along any of the directions in $\{-1, 0, 1\}^d \setminus \{\mathbf{0}\}$ in a large $d$-dimensional grid (as in a word search)? Patchell and Spiro first posed a version of this question, which Alon and Kravitz completely answered for a large class of "well-behaved" words, including those with no repeated letters. We study the general case, which exhibits greater variety and is often more complicated (even for $d=1$). We also discuss some connections to other problems in combinatorics, including the storied $n$-queens problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_19678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Words with Repeated Letters in a Grid Halberstam, Zachary Schildkraut, Carl Combinatorics 05D99, 05B30, 05A16, 68R05 Given a word $w$, what is the maximum possible number of appearances of $w$ reading contiguously along any of the directions in $\{-1, 0, 1\}^d \setminus \{\mathbf{0}\}$ in a large $d$-dimensional grid (as in a word search)? Patchell and Spiro first posed a version of this question, which Alon and Kravitz completely answered for a large class of "well-behaved" words, including those with no repeated letters. We study the general case, which exhibits greater variety and is often more complicated (even for $d=1$). We also discuss some connections to other problems in combinatorics, including the storied $n$-queens problem. |
| title | Words with Repeated Letters in a Grid |
| topic | Combinatorics 05D99, 05B30, 05A16, 68R05 |
| url | https://arxiv.org/abs/2511.19678 |