@article{10902/24524,
year = {2021},
month = {4},
url = {http://hdl.handle.net/10902/24524},
abstract = {In each dimension d there is a constant woo(d) [épsilon] N such that for every n [épsilon] N all but finitely many lattice d-polytopes with n lattice points have llattice width at most woo(d). We call woo(d) the finiteness threshold width in dimension d and show that d - 2   woo(d)  O _d4/3_. Blanco and Santos determined the value woo(3) = 1. Here, we establish woo(4) = 2. This implies, in particular, that there are only finitely many empty 4-simplices of width larger than two. (This last statement was claimed by Barile et al. in [Proc. Am. Math. Soc. 139 (2011), pp. 4247-4253], but we have found a gap in their proof.) Our main tool is the study of d-dimensional lifts of hollow (d-1)-polytopes.},
organization = {The first and fourth authors were supported by grants MTM2014-54207-P, MTM2017-83750-P, and the first author was also supported by BES-2012-058920 of the Spanish Ministry of Science. The fourth author was also supported by the Einstein Foundation Berlin under grant EVF-2015-230. The third author was supported by the Berlin Mathematical School.},
publisher = {American Mathematical Society},
publisher = {Transactions of the American Mathematical Society, Series. B, 2021, 8,  399-419},
title = {The finiteness threshold width of lattice polytopes},
author = {Blanco Gómez, Mónica and Haase, C. and Hoffman, Jan and Santos, Francisco},
}