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The Euler characteristic, thought of as a function that assigns a numericalvalue to every finite simplicial complex, is locally determined in both acombinatorial sense and a geometric sense. In this note we show that not everyfunction that assigns a numerical value to every finite simplicial complex viaa linear combination of the numbers of simplices in each dimension is locallydetermined in either sense. In particular, the Charney-Davis quantity $\lambda(L)$ is not locally determined in either sense if it is defined on a set ofsimplicial complexes that includes all flag spheres of a given odd dimension.

Locally Determined Functions of Finite Simplicial Complexes that are Linear Combinations of the Numbers of Simplices in Each Dimension