Many regular triangulations and many polytopes

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URI: https://hdl.handle.net/10902/32826
ISSN: 0025-5831
ISSN: 1432-1807
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Autoría
Padrol, Arnau; Philippe, Eva; Santos, FranciscoAutoridad Unican
Fecha
2024
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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Mathematische Annalen, 2024, 389(1), 745-763
Editorial
Springer
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Resumen/Abstract
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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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.