Enumeration in convex geometries and associated polytopal subdivisions of spheres

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We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The complete information on the numbers of faces and chains of faces in these spheres can be obtained from the defining lattices in a manner analogous to the relation between arrangements of hyperplanes and their underlying geometric intersection lattices.
18 pages, 4 figures; incorporates suggestions by referees; minor revisions throughout; expanded discussion on chain enumeration in last section; to be published in Discrete and Computational Geometry

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Combinatorics, 05E99, 06A07, 52B05, 52B40 (primary); 06B99, 52C40 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/101307

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505576
 http://arxiv.org/abs/math/0505576

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arXiv