超八面体物种
Hyperoctahedral species
摘要：
我们引入了一个新的定义的物种类型B，或H-物种，类似于经典物种（类型A），但我们认为的行动组Bn的签署置换。我们感兴趣的是这些H-物种的代数结构，并给出例子的霍普夫幺半群。本文给出了从一个物种得到一个分次向量空间的自然方法，这将使我们加深对这些物种的理解。特别地，集合复合的经典类在给定函子下的象同构于组合霍普夫代数DQSym.
英文摘要：
We introduce a new definition for the species of type B, or H-species, analog to the classical species (of type A), but on which we consider the action of the groups Bn of signed permutations. We are interested in algebraic structure on these H-species and give examples of Hopf monoids. The natural way to get a graded vector space from a species, given in this paper in terms of functors, will allow us to deepen our understanding of these species. In particular, the image of the classical species of set compositions under a given functor is isomorphic to the combinatorial Hopf algebra DQSym.
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