Abstract
In 1987 Kalai presented a new proof of the Lower Bound Theorem for simplicial convex d-polytopes by linking the problem to results in rigidity and stress. He suggested that if higher-dimensional analogues of stress and rigidity were developed, they might lead to other combinatorial results on polytopes, and in particular another proof of the g-Theorem. Here we discuss such a generalization of stress and its relationship to face rings, h-vectors, shellings, bistellar operations, spheres, and simplicial polytopes. In particular, stress plays a role in McMullen’s recent new geometric proof of the g-Theorem using his polytope algebra.
Supported in part by NSF grants DMS-8504050 and DMS-8802933, by NSA grant MDA904-89-H-2038, by the Mittag-Leffler Institute, and by DIM ACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, NSF-STC88-09648.
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Lee, C.W. (1994). Generalized Stress and Motions. In: Bisztriczky, T., McMullen, P., Schneider, R., Weiss, A.I. (eds) Polytopes: Abstract, Convex and Computational. NATO ASI Series, vol 440. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0924-6_12
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DOI: https://doi.org/10.1007/978-94-011-0924-6_12
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