论文标题
部分可观测时空混沌系统的无模型预测
On isomorphism classes of leaf-induced subtrees in topological trees
论文作者
论文摘要
可以通过生根树的叶子子集以自然的方式诱导子树。我们研究了没有顶点1（拓扑树）的根树的叶（叶引起的子树）引起的非同态子树的数量。我们表明，只有恒星和二进制毛毛虫在所有拓扑树中具有最小的非形态叶子引起的子树，并具有给定数量的叶子。我们为$ d $ ar的毛毛虫和完整的$ d $ are树的家庭获得了一个封闭式和递归公式。使用多项式复发发现了针对完整的$ d $ are树的渐近公式。我们还表明，完整的高度二进制树$ h> 1 $完全包含$ \ lfloor 2（1.24602 ...）^{2^h} \ rfloor $ nonisomorphic foldomorphic诱导的子树。
A subtree can be induced in a natural way by a subset of leaves of a rooted tree. We study the number of nonisomorphic such subtrees induced by leaves (leaf-induced subtrees) of a rooted tree with no vertex of outdegree 1 (topological tree). We show that only stars and binary caterpillars have the minimum nonisomorphic leaf-induced subtrees among all topological trees with a given number of leaves. We obtain a closed formula and a recursive formula for the families of $d$-ary caterpillars and complete $d$-ary trees, respectively. An asymptotic formula is found for complete $d$-ary trees using polynomial recurrences. We also show that the complete binary tree of height $h>1$ contains precisely $\lfloor 2(1.24602...)^{2^h}\rfloor$ nonisomorphic leaf-induced subtrees.
