离散几何的两个铺砌问题

Two Problems about Tiling in Discrete Geometry

利用图论和代数的方法研究离散几何中的两个铺砌问题:1)给出1×2长方形铺砌多米诺骨牌的充分必要条件;2)对高维空间盒子的情形,给出m_1×m_2×…×m_n砖能够铺砌a_1×a_2×…×a_n盒子的一些必要条件和充要条件.

We consider two problems about tiling in discrete geometry. 1） A sufficient and necessary condition that a 1 × 2 rectangle can tile a polyomino is given; 2） The problem of tiling boxes with congruent bricks in high dimensional spaces is discussed. Some necessary conditions about tiling a1×a2×…×an box with m1×m2×m…×mn bricks are given.