论文标题
避免了一组小图案的选票排列的完整枚举
A Complete Enumeration of Ballot Permutations Avoiding Sets of Small Patterns
论文作者
论文摘要
前缀包含至少与下降一样多的置换称为选票排列。 Lin，Wang和Zhao先前已经列举了避免少量图案的投票排列，并提出了枚举投票排列的问题，避免了一对长度为3美元的排列。我们完全列举投票排列，避免了两种长度$ 3 $的模式，我们将这些回避类别与各自的复发关系和公式联系起来，这导致投票排列之间的有趣的两者避免避免$ 132 $和312美元与戴克路径的左侧因素。此外，我们还得出结论，避免了两种长度$ 3 $的投票排列的WILF分类，然后我们将结果扩展到完全枚举投票排列，避免了三种长度的$ 3 $。
Permutations whose prefixes contain at least as many ascents as descents are called ballot permutations. Lin, Wang, and Zhao have previously enumerated ballot permutations avoiding small patterns and have proposed the problem of enumerating ballot permutations avoiding a pair of permutations of length $3$. We completely enumerate ballot permutations avoiding two patterns of length $3$ and we relate these avoidance classes with their respective recurrence relations and formulas, which leads to an interesting bijection between ballot permutations avoiding $132$ and $312$ with left factors of Dyck paths. In addition, we also conclude the Wilf-classification of ballot permutations avoiding sets of two patterns of length $3$, and we then extend our results to completely enumerate ballot permutations avoiding three patterns of length $3$.
