论文标题
双公共HOPF代数的图形签名
Signatures of graphs for bicommutative Hopf algebras
论文作者
论文摘要
本文根据图形组合代数定义的签名型函数来计算子图的计数。然后，在计数子图的背景下出现的众所周知的代数身份被其角色属性和一种“陈的身份”所捕获。虽然子图（和同构）的不同概念对应于图上的不同组合HOPF代数，但我们将证明它们与多项式HOPF代数同构。此外，HOPF代数之间的异构化可以通过尊重计数操作的地图来实现。
This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that arise in the context of counting subgraphs are then captured by their character property and a type of "Chen's identity". While different notions of subgraphs (and homomorphisms) correspond to different combinatorial Hopf algebras on graphs, we will show that they are all isomorphic to a polynomial Hopf algebra. In addition, the isomorphy between the Hopf algebras can be realized by maps that respect the counting operations.
