论文标题
八次八次超图，共同分析和色度评估的双重双齿
Eight times four bialgebras of hypergraphs, cointeractions, and chromatic polynomials
论文作者
论文摘要
我们考虑了超图的双齿，这是施密特的hopf代数的概括，并表明它具有共同的bialgebra。因此，从L. foissy的意义上讲，一个人具有双重双重性，他最近证明了当时在多项式环$ {\ mathbb q} [x] $上的双重双重双ggebra结构上有独特的双重双ggebra形态。我们显示了与超图相关的多项式是超图形的多项式。 此外，超图发生在四重奏中：有一个双重，补体和双重补体超图。这些对应关系是参与，引起了其他三个双重双齿，另外三个色度评价。总的来说，我们提供了八个四分之一的双重双子，其中包括最近的Aguiar和F. ardila的双齿，以及L. foissy。
We consider the bialgebra of hypergraphs, a generalization of Schmitt's Hopf algebra of graphs, and show it has a cointeracting bialgebra. So one has a double bialgebra in the sense of L. Foissy, who recently proved there is then a unique double bialgebra morphism to the double bialgebra structure on the polynomial ring ${\mathbb Q}[x]$. We show the polynomial associated to a hypergraph is the hypergraph chromatic polynomial. Moreover hypergraphs occurs in quartets: there is a dual, a complement, and a dual complement hypergraph. These correspondences are involutions and give rise to three other double bialgebras, and three more chromatic polynomials. In all we give eight quartets of bialgebras which includes recent bialgebras of M. Aguiar and F. Ardila, and by L. Foissy.
