Many Triangulated 3-Spheres
نویسندگان
چکیده
We construct 2Ω(n 5/4) combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2O(n log n) combinatorial types of simplicial 4-polytopes, this proves that asymptotically, there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988), who had proved a similar statement about d-spheres and (d + 1)polytopes for fixed d ≥ 4. Mathematics Subject Classification (1991): Primary: 52B11, Secondary: 52B70, 57Q15
منابع مشابه
N ov 2 00 3 Many Triangulated 3 - Spheres Julian
We construct 2Ω(n 5/4) combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2O(n logn) combinatorial types of simplicial 4-polytopes, this proves that asymptotically, there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988)...
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تاریخ انتشار 2002