论文标题
WILF等效于植根标记的森林中的图案
Wilf Equivalences for Patterns in Rooted Labeled Forests
论文作者
论文摘要
在Garg和Peng的最新工作中，我们继续对植根森林中的经典和连续模式进行调查，从而解决了他们的一些猜想和问题，并在可能的情况下证明了概括。通过Anders and Archer引入的森林模拟式三脚架的延伸，我们展示了一个新的森林 - 威尔夫等价家族，完成了由长度3和长度模式组成的集合的森林 - 威尔夫等效类别的分类，最多为5美元。 We also find a new family of nontrivial c-forest-Wilf equivalences between single patterns using the forest analogue of the Goulden-Jackson cluster method, showing that a $(1-o(1))^n$-fraction of patterns of length $n$ satisfy a nontrivial c-forest-Wilf equivalence and that there are c-forest-Wilf equivalence classes of patterns of length $n$ of exponential size.此外，我们考虑了Dwyer和Elizalde为置换的超级c-wilf等效性的森林类似物，这表明超级c-c-forest-wilf等价是通过枚举森林群集posets的线性延迟的范围而变得琐碎的。
Building off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests, resolving some of their conjectures and questions and proving generalizations whenever possible. Through extensions of the forest Simion-Schmidt bijection introduced by Anders and Archer, we demonstrate a new family of forest-Wilf equivalences, completing the classification of forest-Wilf equivalence classes for sets consisting of a pattern of length 3 and a pattern of length at most $5$. We also find a new family of nontrivial c-forest-Wilf equivalences between single patterns using the forest analogue of the Goulden-Jackson cluster method, showing that a $(1-o(1))^n$-fraction of patterns of length $n$ satisfy a nontrivial c-forest-Wilf equivalence and that there are c-forest-Wilf equivalence classes of patterns of length $n$ of exponential size. Additionally, we consider a forest analogue of super-strong-c-Wilf equivalence, introduced for permutations by Dwyer and Elizalde, showing that super-strong-c-forest-Wilf equivalences are trivial by enumerating linear extensions of forest cluster posets.
