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arXiv · 2211.14887

Cats in cubes

Noga Alon·Noah Kravitz
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Abstract

Answering a recent question of Patchell and Spiro, we show that when a $d$-dimensional cube of side length $n$ is filled with letters, the word $\mathsf{CAT}$ can appear contiguously at most $(3^{d-1}/2)n^d$ times (allowing diagonals); we also characterize when equality occurs and extend our results to words other than $\mathsf{CAT}$.

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Noga Alon, Noah Kravitz. 2022-11-27. Cats in cubes. https://arxiv.org/abs/2211.14887

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