2 citations · 3 across the 4 of their papers we have counts for
4 papers
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^…
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..…
Polyboxes, cube tilings and rigidity
Andrzej P. Kisielewicz, Krzysztof Przesławski
A non-empty subset A of X = X_1 x...x X_d is a (proper) box if A = A_1 x...x A_d and A_i is a (proper) subset of X_i for each i. Suppose that for each pair of boxes A, B and each i…
Rigidity and the chess board theorem for cube packings
Andrzej P. Kisielewicz, Krzysztof Przesławski
Each packing of R^d by translates of the unit cube [0,1)^d admits a decomposition into at most two parts such that if a translate of the unit cube is covered by one of them, then i…