论文标题
方格的独立复合体的拓扑结构
The topology of independence complexes of square grids
论文作者
论文摘要
图G的独立配合物是一种简单的复合物，其简单是G中的独立集。在过去的几十年中，正方形网格的独立性复合物（具有各种边界条件）由于与统计物理的硬方形模型的联系而引起了很多关注。在本文中，我们证明，如果G是带有开放或圆柱边界条件的$ M \ times n $网格，那么其独立络合物是同质的，等同于楔形球体。该结果的一部分解决了Iriye的猜想。
The independence complex of a graph G is a simplicial complex whose simplices are the independent sets in G. In the last couple of decades, the independence complexes of square grids (with various boundary conditions) have gained much attention because of their connections with the hard square model from statistical physics. In this article, we prove that if G is an $m\times n$ grid with open or cylindrical boundary condition then its independence complex is homotopy equivalent to a wedge of spheres. A part of this result settles a conjecture of Iriye.
