关于盒子划分成盒子的组合问题
On combinatorial problem concerning partitions of a box into boxes
摘要：
我们考虑将R^n中的n维盒子划分成有限个内部两两不相交的盒子。研究了具有性质（W_n）的集合X \subseteq（0，\infty）：对任意n维盒P和P的任意划分，如果每个组成盒都有一条边长属于X，则P的一条边长属于X.证明了集合X \subseteq（0，\infty）具有性质（W_n）当且仅当X关于运算x+y和x+y+z-2 min（x，y，z）是闭的.
英文摘要：
We consider partitions of n-dimensional boxes in R^n, n>1, into a finite number of boxes with pairwise disjoint interiors. We study sets X \subseteq (0,\infty) with the Property (W_n): for every n-dimensional box P and every partition of P, if each constituent box has one side with the length belonging to X, then the length of one side of P belongs to X. We prove that the set X \subseteq (0,\infty) has Property (W_n) if and only if X is closed with respect to the operations: x+y and x+y+z-2min(x,y,z).
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