2017/10/24 by Averkov, Gennadiy, Krümpelmann, Jan, Nill, Benjamin
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1710.08646
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.