Multi-tiling and equidecomposability of polytopes by lattice translates
Combinatorics
2019-10-30 v2 Classical Analysis and ODEs
Metric Geometry
Abstract
We characterize the polytopes in (not necessarily convex or connected ones) which multi-tile the space by translations along a given lattice. We also give a necessary and sufficient condition for two polytopes in to be equidecomposable by lattice translations.
Cite
@article{arxiv.1804.09920,
title = {Multi-tiling and equidecomposability of polytopes by lattice translates},
author = {Nir Lev and Bochen Liu},
journal= {arXiv preprint arXiv:1804.09920},
year = {2019}
}
Comments
To appear in the Bulletin of the London Mathematical Society