Title: Bounding the number of holes required for folding rectangular polyominoes into cubes Show Chinese title

Title: 限定折叠矩形多米诺 into 立方体所需的孔数

Abstract: We study the problem of whether rectangular polyominoes with holes are cube-foldable, that is, whether they can be folded into a cube, if creases are only allowed along grid lines. It is known that holes of sufficient size guarantee that this is the case. Smaller holes which by themselves do not make a rectangular polyomino cube-foldable can sometimes be combined to create cube-foldable polyominoes. We investigate minimal sets of holes which guarantee cube-foldability. We show that if all holes are of the same type, the these minimal sets have size at most 4, and if we allow different types of holes, then there is no upper bound on the size. Show Chinese abstract

Abstract: 我们研究了带有孔的矩形多米诺骨牌是否可以折叠成一个立方体的问题，即仅允许沿网格线折叠时，它们是否可以折叠成一个立方体。 已知足够大的孔可以保证这一点。 单独本身不能使矩形多米诺骨牌可折叠成立方体的较小孔有时可以组合起来创建可折叠成立方体的多米诺骨牌。 我们研究了保证可折叠性的最小孔集。 我们证明，如果所有孔类型相同，这些最小集合的大小最多为4，而如果我们允许不同类型的孔，则没有大小上限。