Lattice Simplices with a Fixed Positive Number of Interior Lattice Points: A Nearly Optimal Volume Bound

被引：4

作者：

Averkov, Gennadiy ^{[1
]}

Krumpelmann, Jan ^{[1
]}

Nill, Benjamin ^{[1
]}

机构：

[1] Otto von Guericke Univ, Fac Math, Univ Pl 2, D-39106 Magdeburg, Germany

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2020年 / 2020卷 / 13期

关键词：

POLYTOPES;

D O I：

10.1093/imrn/rny130

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：3871 / 3885

页数：15

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