Lattice simplices with a fixed positive number of interior lattice points: A nearly optimal volume bound
Combinatorics
2017-10-25 v1 Algebraic Geometry
Metric Geometry
Optimization and Control
Abstract
We give an explicit upper bound on the volume of lattice simplices with fixed positive number of interior lattice points. The bound differs from the conjectural sharp upper bound only by a linear factor in the dimension. This improves significantly upon the previously best results by Pikhurko from 2001.
Keywords
Cite
@article{arxiv.1710.08646,
title = {Lattice simplices with a fixed positive number of interior lattice points: A nearly optimal volume bound},
author = {Gennadiy Averkov and Jan Krümpelmann and Benjamin Nill},
journal= {arXiv preprint arXiv:1710.08646},
year = {2017}
}