标题： 有界格子瓷砖与另一个格子的密铺 显示英文标题

标题： Bounded lattice tiles that pack with another lattice

摘要： 假设L和M是欧几里得空间中的满秩格，使得vol(L) < vol(M)。 回答Han和Wang在2001年提出的问题，我们展示了如何构造一个有界可测集F（我们可以甚至取F为有限个多面体的并集），使得F+L是一个密铺，F+M是一个覆盖。 如果我们不要求F的可测性，通常可以找到一个集F，它与L和M都能密铺，即使L和M的体积不同，例如当它们的交只是平凡的时候。 我们还在这里证明，如果L和M的体积不同，这样的集F永远不可能是有界的。 显示英文摘要

摘要： Suppose L and M are full-rank lattices in Euclidean space, such that vol(L) < vol(M). Answering a question of Han and Wang from 2001, we show how to construct a bounded measurable set F (we can even take F to be a finite union of polytopes) such that F+L is a tiling and F+M is a packing. If we do not require measurability of F it is often possible that a set F can be found tiling with both L and M even when L and M have different volumes, for instance if their intersection is trivial. We also show here that such a set can never be bounded if L and M have different volumes.