论文标题
通过（数字和符号）动态编程自动计数受限制的Dyck路径
Automatic Counting of Restricted Dyck Paths via (Numeric and Symbolic) Dynamic Programming
论文作者
论文摘要
Dyck路径是列举组合学中最重要的对象之一，并且有许多论文专门计算选定的戴克路径家族。在这里，我们提出了两种方法，用于使用“愚蠢”方法（由数字动态编程驱动）的许多此类家庭的自动计数，这些方法通常在实践中起作用，以及一种由“符号”动态编程驱动的“聪明”方法，是更大问题所需的“聪明”方法。两种方法都是完全自动化的，并在枫树中实现。
Dyck paths are one of the most important objects in enumerative combinatorics, and there are many papers devoted to counting selected families of Dyck paths. Here we present two approaches for the automatic counting of many such families, using both a "dumb" approach (driven by numeric dynamic programming) that often works in practice, and a "clever" approach, needed for larger problems, driven by "symbolic" dynamic programming. Both approaches are fully automated and implemented in Maple.
