一类图构形的特征多项式

The Characteristic Polynomials of a Class of Graphical Arrangements

超平面构形是奇点理论的一个分支,它是一类具有非孤立奇点的超曲面。超平面构形是处在组合学、代数学、拓扑学、代数几何学等多个学科交汇处的一门年轻的学科,它的巨大魅力在于:能从组合学以及代数学等不同角度去描述它的拓扑不变量。特征多项式作为构形的一个组合不变量,在构形组合、代数、拓扑性质的研究中,起到非常重要的作用。本文利用图论中的顶点着色理论给出一类特殊图构形的特征多项式。

The arrangement of hyperplanes,which is a branch of singularity theory,is a hypersurface with non-isolated singularities. The arrangement of hyperplanes is a new interdisciplinary field which comes from combinatorics,algebra,topology,algebraic geometry and so on. The greatest charm of the theory of hyperplane arrangements is expressing topological invariants of the complement space in terms of combinatorics and algebra. The characteristic polynomials are combinatorial invariants for hyperplane arrangements,and play important roles in the studying of the properties of the aspects of combinatorics,algebra and topology. In this paper,the characteristic polynomials of a class of graphical arrangements are established by the chromatic theory of the vertices graphs.