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arXiv · 0809.1960

Keller's Conjecture on the Existence of Columns in Cube Tilings of R^n

Magdalena Łysakowska·Krzysztof Przesławski
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Abstract

It is shown that if n<7, then each tiling of R^n by translates of the unit cube [0,1)^n contains a column; that is, a family of the form {[0,1)^n+(s+ke_i): k \in Z}, where s \in R^n, e_i is an element of the standard basis of R^n and Z is the set of integers.

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Magdalena Łysakowska, Krzysztof Przesławski. 2008-09-11. Keller's Conjecture on the Existence of Columns in Cube Tilings of R^n. https://arxiv.org/abs/0809.1960

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