论文标题
自动计数受限的Motzkin路径
Automated Counting of Restricted Motzkin Paths
论文作者
论文摘要
Motzkin路径是简单而重要的组合对象。在本文中，我们考虑了Motzkin路径的家族，对峰值高度，山谷高度，向上的长度，向下行驶的长度和平坦长度有限制。本文提出了两种全自动方法，用于列举此类家庭的路径。第一个方法使用数字动态编程。尽管这种方法通常有时有效，但它可能会很慢，并且可能对更大的问题不起作用。第二种方法使用符号动态编程来解决此类问题。这些方法是在本文随附的枫木软件包中实现的。
Motzkin paths are simple yet important combinatorial objects. In this paper, we consider families of Motzkin paths with restrictions on peak heights, valley heights, upward-run lengths, downward-run lengths, and flat-run lengths. This paper presents two fully automated methods for enumerating the paths of such families. The first method uses numeric dynamic programming. While this method often times works, it can be slow and may not work for larger problems. The second method uses symbolic dynamic programming to solve such problems. These methods are implemented in the maple packages accompanying this article.
