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.
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页码：3871 / 3885
页数：15
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