Cats in cubes

Noga Alon; Noah Kravitz

doi:10.37236/11735

Cats in cubes

Noga Alon
, Noah Kravitz

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Article number	P3.29
Journal	Electronic Journal of Combinatorics
Volume	31
Issue number	3
DOIs	https://doi.org/10.37236/11735
State	Published - 1 Jan 2024
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/11735

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AB - Answering a recent question of Patchell and Spiro, we show that when a ddimensional cube of side length n is filled with letters, the word CAT can appear contiguously at most (3d−1/2)nd times (allowing diagonals); we also characterize when equality occurs (in the toroidal analogue of the problems) and extend our results to words other than CAT.

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Cats in cubes

Abstract

ASJC Scopus subject areas

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