@article{10902/32826,
year = {2024},
url = {https://hdl.handle.net/10902/32826},
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.},
organization = {Work of Padrol and Philippe is supported by grants ANR-17-CE40-0018 and ANR-21-CE48-0020 of the French National Research Agency ANR (projects CAPPS and PAGCAP). Work of Padrol and Santos is supported by grant PID2019-106188GB-I00 of MCIN/AEI/10.13039/501100011033 and project CLaPPo (21.SI03.64658) of Universidad de Cantabria and Banco Santander.},
publisher = {Springer},
publisher = {Mathematische Annalen, 2024, 389(1), 745-763},
title = {Many regular triangulations and many polytopes},
author = {Padrol, Arnau and Philippe, Eva and Santos, Francisco},
}