Abstract
We describe here the notion of generalized stress on simplicial complexes, which serves several purposes: it establishes a link between two proofs of the Lower Bound Theorem for simplicial convex polytopes; elucidates some connections between the algebraic tools and the geometric properties of polytopes; leads to an associated natural generalization of infinitesimal motions; behaves well with respect to bistellar operations in the same way that the face ring of a simplicial complex coordinates well with shelling operations, giving rise to a new proof that p.l.-spheres are Cohen-Macaulay; and is dual to the notion of McMullen's weights on simple polytopes which he used to give a simpler, more geometric proof of theg-theorem.
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Supported in part by NSF Grants DMS-8504050 and DMS-8802933, by NSA Grant MDA904-89-H-2038, by the Mittag-Leffier Institute, by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, NSF-STC88-09648, and by a grant from the EPSRC.
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Lee, C.W. P.L.-Spheres, convex polytopes, and stress. Discrete Comput Geom 15, 389–421 (1996). https://doi.org/10.1007/BF02711516
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DOI: https://doi.org/10.1007/BF02711516