Keller properties for integer tiling

2024/04/18 by Bruce, Benjamin, Laba, Izabella
#05B45 #52C22 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.12518

Abstract

Keller's conjecture on cube tilings asserted that, in any tiling of ℝ^d by unit cubes, there must exist two cubes that share a (d-1)-dimensional face. This is now known to be true in dimensions d≤ 7 and false for d≥ 8. In this article, we investigate analogues of Keller's conjecture for integer tilings.

Related

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• On Keller's conjecture in dimension seven