布尔复形的同调
Homology of the Boolean Complex
摘要：
我们构造和分析了一个明确的基础上的同源性的Coxeter系统的布尔复形。这给出了组合意义的领域楔形和描述同伦类型的复杂。我们给任意有限单图赋予一组乱序。对于每一个错乱，我们在复形的同调中构造一个相应的元素，这些元素的集合形成布尔复形的同调的基础。在这种方式下，楔形和中描述复形同伦类型的球面可以用一组无序来表示。我们给出了一个明确的，封闭形式的描述，可以从任何图形的乱序，并计算这组几个家庭的图。在完全图和Ferrers图的情况下，这些计算给出了以前得到的计数结果的双射证明。
英文摘要：
We construct and analyze an explicit basis for the homology of the boolean complex of a Coxeter system. This gives combinatorial meaning to the spheres in the wedge sum describing the homotopy type of the complex. We assign a set of derangements to any finite simple graph. For each derangement, we construct a corresponding element in the homology of the complex, and the collection of these elements forms a basis for the homology of the boolean complex. In this manner, the spheres in the wedge sum describing the homotopy type of the complex can be represented by a set of derangements. We give an explicit, closed-form description of the derangements that can be obtained from any graph, and compute this set for several families of graphs. In the cases of complete graphs and Ferrers graphs, these calculations give bijective proofs of previously obtained enumerative results.
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