论文标题
Associahedra，Cyclohedra和Power系列反转
Associahedra, cyclohedra and inversion of power series
论文作者
论文摘要
我们介绍了一组循环和路径集的Hopf Monoid，其中包含faàdibruno hopf monoid作为下monoid。我们为其对立的无取消和无分组公式，一个在管道方面，一个在\ emph {尖}的非交叉分区方面。我们提供了有关功率系列的Hopf Monoid角色组的明确描述。我们使用图形辅助方法将路径和周期分别与Associahedra和Cyclohedra相关联。我们根据这些多面体的面部对角色组的反演进行了反演的公式。
We introduce the Hopf monoid of sets of cycles and paths, which contains the Faà di Bruno Hopf monoid as a submonoid. We give cancellation-free and grouping-free formulas for its antipode, one in terms of tubings and one in terms of \emph{pointed} noncrossing partitions. We provide an explicit description of the group of characters of this Hopf monoid in terms of pairs of power series. Using graph associahedra, we relate paths and cycles to associahedra and cyclohedra, respectively. We give formulas for inversion in the group of characters in terms of the faces of these polytopes.
