The sum of entries in the inverse of the intersection matrix of a simplicial complex equals its Euler characteristic, and so does the difference between the numbers of positive and negative eigenvalues of that matrix.
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In this note we revisit a "ring of graphs" Q in which the set of finite simple graphs N extend the role of the natural numbers and the signed graphs Z extend the role of the integers. We point out the existence of a norm which allows to complete Q to a real or complex Banach algebra R or C.
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The energy of a simplicial complex
The sum of entries in the inverse of the intersection matrix of a simplicial complex equals its Euler characteristic, and so does the difference between the numbers of positive and negative eigenvalues of that matrix.