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arXiv · 2511.19678

Words with Repeated Letters in a Grid

Zachary Halberstam·Carl Schildkraut
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Abstract

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.

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Zachary Halberstam, Carl Schildkraut. 2025-11-26. Words with Repeated Letters in a Grid. https://arxiv.org/abs/2511.19678

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