Many neighborly inscribed polytopes and Delaunay triangulations
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چکیده
We present a very simple explicit technique to generate a large family of point configurations with neighborly Delaunay triangulations. This proves that there are superexponentially many combinatorially distinct neighborly d-polytopes with n vertices that admit realizations inscribed on the sphere. These are the first examples of inscribable neighborly polytopes that are not cyclic polytopes, and provide the current best lower bound for the number of combinatorial types of inscribable polytopes (and thus also of Delaunay triangulations). It coincides with the current best lower bound for the number of combinatorial types of polytopes. Résumé. Nous présentons une technique explicite simple pour générer une large famille de configurations de points dont les triangulations de Delaunay sont neighborly. Cela prouve que le nombre de d-polytopes combinatoirement distincts avec n sommets et admettant une réalization inscrite sur la sphère est surexponentiel. Ce sont les premiers exemples de polytopes inscriptibles neighborly qui ne sont pas des polytopes cycliques et ils donnent la meilleure borne inférieure actuelle pour le nombre de types combinatoires de polytopes inscriptibles (et donc aussi de triangulations de Delaunay). Cette borne coı̈ncide avec la meilleure borne inférieure actuelle pour le nombre de types combinatoires de polytopes.
منابع مشابه
Neighborly inscribed polytopes and Delaunay triangulations
We prove that there are superexponentially many combinatorially distinct d-dimensional neighborly Delaunay triangulations on n points. These are the first examples of neighborly Delaunay triangulations that cannot be obtained via a stereographic projection of an inscribed cyclic polytope, and provide the current best lower bound for the number of combinatorial types of Delaunay triangulations. ...
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تاریخ انتشار 2014