English

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 Rd\mathbb{R}^d (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 Rd\mathbb{R}^d to be equidecomposable by lattice translations.

Keywords

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