论文信息 - Neighborly cubical spheres and a cubical lower bound conjecture

Neighborly cubical spheres and a cubical lower bound conjecture

Using mirrors and cyclic polytopes, we construct cubicald-spheres which are the analogs of cyclic polytopes in the sense that they have the ⌉d−1/2⌈-skeleta of cubes. The existence of these neighborly cubical spheres leads to a special case of an upper bound conjecture for cubical spheres, suggested by Kalai. We extend the same construction to show that the closed convex hull off-vectors of cubical spheres contains a cone described by Adin, as an analog to the generalized lower bound theorem for simplicial polytopes.

Louis J. Billera | Eric K. Babson | Clara S. Chan

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