Year: 2010
Type: preprint
Abstract: Our earlier article proved that if $n > 1$ translates of sublattices of $Z^d$ tile $Z^d$, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. We re-prove this Theorem, this time using generating functions. We also show that for $d \geq 1$, not every finite tiling of $Z^d$ by lattices can be obtained from the trivial tiling by the process of repeatedly subdividing a tile into sub-tiles that are translates of one another.
Source: arXiv (Cornell University)
Authors: Feldman, David, Propp, James, Robins, Sinai
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394654283