Combinatorial Laplacians of matroid complexes
Combinatorial Laplacians of matroid complexes
复制标题
拟阵复合体的组合拉普拉斯算子
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
D. Stanton
中科院分区：
文献类型：
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作者：
W. Kook;V. Reiner;D. Stanton
对于任意有限单纯复数K，我们可以定义拉普拉斯算子∆I，它是黎曼流形上微分形式上的拉普拉斯算子的组合类比。定义(如[6，7])如下。设Ci是K中具有实系数的(定向)单纯I-链的R-向量空间，∂i：Ci→Ci−1是通常的单纯边界映射.通过声明定向单形来赋予词一个内积，从而形成词的一个标准正交基，从而使我们可以将词与其对偶C∗I联系起来。∂I关于这个内积的伴随是转置∂I或上边界映射δI−1：Ci−1→Ci。定义∆i：Ci→Ci by∆i=δi−1∂i+∂i+1δi。
For any finite simplicial complex K, one can define Laplace operators ∆i which are combinatorial analogues of the Laplace operators on differential forms for a Riemannian manifold. The definition (as in [6, 7]) is as follows. Let Ci be the R-vector space of (oriented) simplicial i-chains in K with real coefficients, and ∂i : Ci → Ci−1 the usual simplicial boundary map. Endow Ci with an inner product by declaring the oriented simplices to form an orthonormal basis of Ci, so that we may identify Ci with its dual C∗ i . The adjoint to ∂i with respect to this inner product is the transpose ∂ i or the coboundary map δi−1 : Ci−1 → Ci. Define ∆i : Ci → Ci by ∆i = δi−1∂i + ∂i+1δi.