论文标题
INFIMA封闭式套装数量最少的树木
Trees with minimum number of infima closed sets
论文作者
论文摘要
令$ t $为根树，而$ v（t）$它的顶点集。 $ v（t）$的子集$ x $被称为$ t $的Infima封闭套件，如果任何两个顶点$ u，v \ in x $，$ u $的第一个共同祖先和$ v $也是$ x $。本文确定了在给定秩序的所有植根树中，在INVIMA封闭的封闭设置中的树木确定了树木，从而回答了克拉扎尔的问题。结果表明，这些树本质上是完整的二进制树，除了最后层面的顶点。此外，还提供了有关$ n $顶点的树木中最小数量的INVIMA封闭套件的渐近估计。
Let $T$ be a rooted tree, and $V(T)$ its set of vertices. A subset $X$ of $V(T)$ is called an infima closed set of $T$ if for any two vertices $u,v\in X$, the first common ancestor of $u$ and $v$ is also in $X$. This paper determines the trees with minimum number of infima closed sets among all rooted trees of given order, thereby answering a question of Klazar. It is shown that these trees are essentially complete binary trees, with the exception of vertices at the last levels. Moreover, an asymptotic estimate for the minimum number of infima closed sets in a tree with $n$ vertices is also provided.
