The infinitesimal Hopf algebra and the poset of planar forests
The infinitesimal Hopf algebra and the poset of planar forests
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DOI：
10.1007/s10801-008-0163-y
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发表时间：
2008-02
影响因子：
0.8
通讯作者：
L. Foissy
中科院分区：
文献类型：
--
作者：
L. Foissy
引入了平面树的无穷小Hopf代数，推广了非交换Connes-Kreimer Hopf代数的构造。定义了一种非退化配对和对偶基，并给出了这种配对在平面森林顶点上的顺序组合解释。此外，在平面森林集合上的副积和配对也可以用偏序来描述，使其与Tamari偏序同构。作为推论，对偶基可以用Möbius反演来计算。
We introduce an infinitesimal Hopf algebra of planar trees, generalising the construction of the non-commutative Connes-Kreimer Hopf algebra. A non-degenerate pairing and a dual basis are defined, and a combinatorial interpretation of the pairing in terms of orders on the vertices of planar forests is given. Moreover, the coproduct and the pairing can also be described with the help of a partial order on the set of planar forests, making it isomorphic to the Tamari poset. As a corollary, the dual basis can be computed with a Möbius inversion.