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

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

2008-09-11

arxiv.org/abs/0809.1960v1

Mathematics

Combinatorics

25 pages

Scientific paper

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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