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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168902It 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.25 pagesCombinatoricsMetric Geometry52C22; 05B45Keller's Conjecture on the Existence of Columns in Cube Tilings of R^ntext