正则分划D^r的存在性

Existence of regular partition Dr

根据Ｅｋ的正则分划Ｄｒ的阶数ｒ以及满足正则分划定义的直接分划的个数ｍ与ｋ的关系，给出了两个主要结果：（１）当ｒｍ＞ｋ时，Ｅｋ不存在正则分划；（２）当ｒｍ≤足时，Ｅｋ一定存在正则分划Ｄｒ．并给出了Ｅｋ，当ｋ≤５时的正则分划的实例计算．

By the relation of r,m and k where r is the rank of regular partition of Ek and m is the number of direct partitions that satisfy the definition of regular partition; two main results are obtained:(1)if rm>k, then the regular partition of Ek does not exist.(2)if rm≤k, then regular partitions of Ek must exist. In addition, the computable examples of regular partition of Ek is given with k≤5.