SOME ENUMERATION CHARACTERISTICS OF RECURSIVE TREES
递归树的若干枚举特征

Recursive tree is defined by Meir and Moon as the variety of non-planarincreasing tree such that all node degrees are allowed. This paper provides a 1-1 correspondence between recursive trees, with size n and leaf number k, and permutations, with size n-l and run number k.Various enumeration characteristics of recursive tree, such as classifying enumeration of nodes (internal nodes and leaves, even and odd nodes, nodes with different out-degrees) and path lengths (according to different node classifications) are investigated, and the corresponding exact enumerating formulas and asymptotic behaviour are given.