不交叉无圈有向图的列表
Tabulation of Noncrossing Acyclic Digraphs
摘要：
我提出了一个算法，给定一个数$n \geq 1$，计算一个紧凑的表示的集合的所有非交叉无环有向图与$n$节点。这种紧凑的表示可以用作这些图上的各种动态规划算法的基础。作为一个例子，随着这篇笔记，我发布了一个算法的实现，用于计算给定大小的非交叉无圈有向图的数量。同样的表格可以被修改来计算其他类别的组合结构，包括弱连接非交叉无环有向图，一般非交叉有向图，非交叉无向图。
英文摘要：
I present an algorithm that, given a number $n \geq 1$, computes a compact representation of the set of all noncrossing acyclic digraphs with $n$ nodes. This compact representation can be used as the basis for a wide range of dynamic programming algorithms on these graphs. As an illustration, along with this note I am releasing the implementation of an algorithm for counting the number of noncrossing acyclic digraphs of a given size. The same tabulation can be modified to count other classes of combinatorial structures, including weakly connected noncrossing acyclic digraphs, general noncrossing digraphs, noncrossing undirected graphs.
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