P.L.-Spheres,convex polytopes,and stress |
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Authors: | C W Lee |
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Institution: | (1) Department of Mathematics, University of Kentucky, 40506 Lexington, KY, USA |
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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.
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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