On a Discrete Version of Alexandrov's Projection Theorem

作     者：Huan XIONG 

作者机构：School of Mathematical SciencesPeking University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2013年第29卷第8期

页      面：1597-1606页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by National 973 Project (Grant No.2011CB808003) National Natural Science Foundation ofChina (Grant No.11131001) 

主　　题：Aleksandrov's projection theorem convex lattice set discrete geometry 

摘      要：In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov＇s projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.