论文标题
在平面树和排列上的Hopf代数
Hopf algebras on planar trees and permutations
论文作者
论文摘要
我们将植根的平面树的空间赋予了Hopf代数的结构。我们证明，这种结构的变化导致霍普夫代数在标记的树木，$ n $ - 树木，增加的平面树和排序的树上。这些结构用于在不同类型的排列上构建HOPF代数。特别是，我们通过平面生根的树木获得了马尔维托托（Malvenutauer）和洛迪（Loday）的Hopf代数 - 鲁特纳（Reutenauer）和洛迪（Loday）的新特征。
We endow the space of rooted planar trees with an structure of Hopf algebra. We prove that variations of such a structure lead to Hopf algebras on the spaces of labelled trees, $n$--trees, increasing planar trees and sorted trees. These structures are used to construct Hopf algebras on different types of permutations. In particular, we obtain new characterizations of the Hopf algebras of Malvenuto--Reutenauer and Loday--Ronco via planar rooted trees.
