论文标题
组合树模型的停车功能品种
Parking function varieties for combinatorial tree models
论文作者
论文摘要
我们研究了最近引入的不同类型的树木停车功能的枚举问题，称为树停车功能，树木停车场，主要的树木停车功能和主要的树停车场分布，用于扎根的重要组合树家庭的树木，包括标有订购，无序和二元树。使用基础结构的组合分解，在求解所得的方程后，对此类树式停车功能的合适生成功能的隐性表征，用于$ n $ $ n $ and $ n $成功驱动器的树木停车功能，从中我们获得精确的和渐近的枚举结果。该方法可以扩展到针对$ n $ $ n $和$ m <n $驱动器的树木停车功能的一般状况\ frac {m} {n} <1 $。
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted labelled trees of important combinatorial tree families including labelled ordered, unordered and binary trees. Using combinatorial decompositions of the underlying structures yields, after solving the resulting equations, implicit characterizations of suitable generating functions of the total number of such tree parking functions for trees of size $n$ and $n$ successful drivers, from which we obtain exact and asymptotic enumeration results. The approach can be extended to the general situation of tree parking functions for trees of size $n$ and $m<n$ drivers for which we are also able to characterize the generating functions solutions, which allow, by applying analytic combinatorics techniques, a study of the asymptotic behaviour of the total number of tree parking functions and distributions for $n \to \infty$ depending on the load factor $0 < α= \frac{m}{n} < 1$.
