Multi-tiling and equidecomposability of polytopes by lattice translates

17 Sep 2019 Lev Nir Liu Bochen

We characterize the polytopes in $\mathbb{R}^d$ (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 $\mathbb{R}^d$ to be equidecomposable by lattice translations...

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Categories


  • COMBINATORICS
  • CLASSICAL ANALYSIS AND ODES
  • METRIC GEOMETRY