论文标题
关于计算三维加泰罗尼亚单词的堤防路径的新统计数据
A new statistic on Dyck paths for counting 3-dimensional Catalan words
论文作者
论文摘要
三维加泰罗尼亚单词是三个字母上的单词，因此任何两个字母上的子字是戴克路径。对于给定的Dyck Path $ d $，最近定义的统计量将加泰罗尼亚单词的数量计入了两个字母上的任何子字的属性，正好是$ d $。在本文中，我们用这种统计数据等于某些值（包括所有素数）列举戴克路径。获得的公式是根据Motzkin数字和Motzkin投票数字。
A 3-dimensional Catalan word is a word on three letters so that the subword on any two letters is a Dyck path. For a given Dyck path $D$, a recently defined statistic counts the number of Catalan words with the property that any subword on two letters is exactly $D$. In this paper, we enumerate Dyck paths with this statistic equal to certain values, including all primes. The formulas obtained are in terms of Motzkin numbers and Motzkin ballot numbers.
