2 papers
math.CO2008★ 2 cited
Keller's Conjecture on the Existence of Columns in Cube Tilings of R^n
Magdalena Łysakowska, Krzysztof Przesławski
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^…
math.CO2008★ 1 cited
The Coin Exchange Problem and the Structure of Cube Tilings
Andrzej P. Kisielewicz, Krzysztof Przesławski
Let k_1,...,k_d be positive integers, and D be a subset of [k_1]x...x[k_d], whose complement can be decomposed into disjoint sets of the form {x_1}x...x{x_{s-1}}x[k_s]x{x_{s+1}}x..…