八分体是覆盖可分解的
Octants are Cover Decomposable
摘要：
我们证明了八分区是覆盖可分解的，即，具有给定八分圆的有限数目平移的空间的任何子集的任何12重覆盖可以被分解成两个覆盖。作为推论，我们得到了平面的任何子集的任何12重覆盖都可以分解为两个覆盖。我们还证明了，任何12重覆盖的整个平面与开放的三角形可以分解成两个覆盖。然而，我们展示了一个不可分解的3重覆盖。
英文摘要：
We prove that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into two coverings. We also show that any 12-fold covering of the whole plane with open triangles can be decomposed into two coverings. However, we exhibit an indecomposable 3-fold covering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
