Abstract
The present paper is motivated by recent work of J. Cheeger, W. Müller, and R. Schrader on the Lipschitz-Killing curvatures of piecewise flat spaces. It is proved that all basic properties of Lipschitz-Killing curvatures can be derived by combinatorial methods using only the Gram-Sommerville and McMullen equations. Angular partially ordered sets yield the appropriate framework for proving the main results by means of the Rota calculus in the incidence algebra of cell complexes.
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