多项式图不变量和KP层次
Polynomial graph invariants and the KP hierarchy
摘要：
我们证明了所有连通图的对称色多项式的生成函数满足（经过适当变量变换）数学物理的Kadomtsev-Petviashvili可积族.此外，我们描述了一个大家庭的多项式图不变量给出相同的解决方案的KP。特别是，我们介绍了阿贝尔多项式的图形，并显示其生成函数。本文的重点是图张成空间上的霍普夫代数结构及其本原空间上的不变量的性质。
英文摘要：
We prove that the generating function for the symmetric chromatic polynomial of all connected graphs satisfies (after appropriate scaling change of variables) the Kadomtsev--Petviashvili integrable hierarchy of mathematical physics. Moreover, we describe a large family of polynomial graph invariants giving the same solution of the KP. In particular, we introduce the Abel polynomial for graphs and show this for its generating function. The key point here is a Hopf algebra structure on the space spanned by graphs and the behavior of the invariants on its primitive space.
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