均匀划分

Uniform partitions

如果一个集合能划分成两两不交且元素个数都相同的一些子集合,则称这些子集合组成原集合的一个均匀划分.Chung-Feller定理证明了自由Dyck路能被均匀划分,而其中一类为Dyck路.本文从Chung-Feller定理及其推广出发,综述关于组合对象的均匀划分的研究成果.

If a set can be partitioned into disjoint subsets which have the same cardinality, then we call the set has a uniform partition. The classic Chung-Feller theorem says that a free Dyck path has a uniform partition, and one of the subsets is a Dyck path. In this paper, from classic Chung-Feller theorem and its generalizations, we survey the research on uniform partitions for combinatorial objects.