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Gaussian Vertex-Face Balance in Random Convex Polyhedra with Fixed Edge Count

Bridges, Lachlan
arXiv (All) · Papers
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combinatoricsprobability
Choose uniformly among the combinatorial types of convex three-dimensional polyhedra with a fixed admissible number $e$ of edges, and let $V_e$ be the number of vertices. This resolves a fixed-edge limit-distribution question posed by Rüdinger: if $β_e=V_e/(e+2)$, then $\sqrt e(β_e-1/2)\Rightarrow N
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