English

Cats in cubes

Combinatorics 2022-11-29 v1

Abstract

Answering a recent question of Patchell and Spiro, we show that when a dd-dimensional cube of side length nn is filled with letters, the word CAT\mathsf{CAT} can appear contiguously at most (3d1/2)nd(3^{d-1}/2)n^d times (allowing diagonals); we also characterize when equality occurs and extend our results to words other than CAT\mathsf{CAT}.

Keywords

Cite

@article{arxiv.2211.14887,
  title  = {Cats in cubes},
  author = {Noga Alon and Noah Kravitz},
  journal= {arXiv preprint arXiv:2211.14887},
  year   = {2022}
}
R2 v1 2026-06-28T07:14:06.442Z