Balanced subdivision and enumeration in balanced spheres |
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| Authors: | Louis J. Billera Katherine E. Magurn |
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| Affiliation: | (1) Department of Mathematics and School of Operations Research, Cornell University, 14853 Ithaca, NY, USA;(2) Department of Mathematics and Statistics, Miami University, 45056 Oxford, OH, USA;(3) Department of Mathematics and Center for Operations Research, Rutgers University, 08903 New Brunswick, NJ, USA |
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| Abstract: | We study here the affine space generated by the extendedf-vectors of simplicial homology (d – 1)-spheres which are balanced of a given type. This space is determined, and its dimension is computed, by deriving a balanced version of the Dehn-Sommerville equations and exhibiting a set of balanced polytopes whose extendedf-vectors span it. To this end, a unique minimal complex of a given type is defined, along with a balanced version of stellar subdivision, and such a subdivision of a face in a minimal complex is realized as the boundary complex of a balanced polytope. For these complexes, we obtain an explicit computation of their extendedh-vectors, and, implicitly,f-vectors.Supported in part by NSF Grant DMS-8403225. |
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