科研之友
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摘要
It is known that the (2k-1)-sphere has at most 2O(n(k) log n) combinatorially distinct triangulations with n vertices, for every k >= 2. Here we construct at least 2 Omega(n(k)) such triangulations, improving on the previous constructions which gave 2 Omega (n(k-1)) in the general case (Kalai) and 2 Omega(n(5/4)) for k >= 2 (Pfeifle-Ziegler). We also construct 2 Omega (n(k-1+1/k)) geodesic (a. k. a. star-convex) n-vertex triangulations of the (2k-1)-sphere. As a step for this (in the case k = 2) we construct n-vertex 4-polytopes containing Omega(n(3/2)) facets that are not simplices, or with Omega(n(3/2)) edges of degree three.
- 出版日期2016-4
