Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第53页
... vertices , A ( G ) has a defining polynomial Q ( A ( G ) ) = П II ( x - xj ) . 1 < i < j≤l Thus A ( G ) is equal to the braid arrangement AR of Definition 1.9 . It follows that an arrangement is graphic if and only if it is a ...
... vertices , A ( G ) has a defining polynomial Q ( A ( G ) ) = П II ( x - xj ) . 1 < i < j≤l Thus A ( G ) is equal to the braid arrangement AR of Definition 1.9 . It follows that an arrangement is graphic if and only if it is a ...
第54页
... vertices and no edges , then there is no restriction for its coloring . Thus we have x ( G , t ) = t ' . Example 2.80 If G is the graph in Figure 2.9 , then there are t ways to color the vertex 1 and there are t - 1 ways to color the ...
... vertices and no edges , then there is no restriction for its coloring . Thus we have x ( G , t ) = t ' . Example 2.80 If G is the graph in Figure 2.9 , then there are t ways to color the vertex 1 and there are t - 1 ways to color the ...
第180页
... vertices with a piecewise linear path . The unbounded edges are paths starting at one vertex and running off to infinity . Addition of a vertex at infinity would make this a graph in the sense of Definition 2.70 . Since the roles of the ...
... vertices with a piecewise linear path . The unbounded edges are paths starting at one vertex and running off to infinity . Addition of a vertex at infinity would make this a graph in the sense of Definition 2.70 . Since the roles of the ...
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A₁ affine arrangement algebra A(A arrangement and let arrangements of hyperplanes assume b₁ basic invariants basis for D(A braid arrangement Brieskorn broken circuit central arrangement chain complex cohomology complement complex reflection groups complexification compute construction Corollary Coxeter group defining polynomial Definition deformation retraction denote dependent exact sequence Example exterior algebra fiber finite follows from Lemma follows from Proposition formula free arrangement free with exp graded K-module graph H₁ H₂ homogeneous homology homotopy type hyperplane arrangement hyperplanes inductively free integers irreducible isomorphism K-algebra ker(x l-arrangement lattice Lemma Let G linear linearly independent Math matrix maximal element Möbius function modular elements module nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Section Shephard groups simplicial space subset subspace supersolvable supersolvable arrangement Suppose surjective topological vertex vertices w₁ write x-independent