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Tag: <span>green function</span>
Home Posts tagged "green function"

Tag: green function

Green Star Formula
discrete geometry, Graph theory

Green Star Formula

By oliverknill January 28, 2018 February 5, 2018  green function, simplicial complex, simplicial complexes

We found a formula of the green function entries g(x,y). Where g is the inverse of the connection matrix of a finite abstract simplicial complex. The formula involves the Euler characteristic of the intersection of the stars of the simplices x and y, hence the name.

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Quest for a Green Function Formula
discrete geometry, Graph theory

Quest for a Green Function Formula

By oliverknill November 26, 2017 November 26, 2017  green function

A simplicial complex G, a finite set of non-empty sets closed under the operation of taking finite non-empty subsets, has the Laplacian $L(x,y) = {\rm sign}(|x \cap y|)$. It is natural as it is always unimodular so that its inverse $g(x,y)$ is always integer valued. In a potential theoretical setup, …

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