English

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}
}