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Article Dans Une Revue Mathematische Annalen Année : 2023

Many regular triangulations and many polytopes

Résumé

We show that for fixed d > 3 and n growing to infinity there are at least (n!)^(d-2±o(1)) different labeled combinatorial types of d-polytopes with n vertices. This is about the square of the previous best lower bounds. As an intermediate step, we show that certain neighborly polytopes (such as particular realizations of cyclic polytopes) have at least (n!)^((d-1)/2 ±o(1)) regular triangulations.
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Dates et versions

hal-04460364 , version 1 (15-02-2024)

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Arnau Padrol, Eva Philippe, Francisco Santos. Many regular triangulations and many polytopes. Mathematische Annalen, 2023, 24 (7), pp.2241-2321. ⟨10.1007/s00208-023-02652-4⟩. ⟨hal-04460364⟩
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