ON INTEGER POINTS IN POLYHEDRA - A LOWER BOUND

被引：19

作者：

BARANY, I

HOWE, R

LOVASZ, L

机构：

[1] MATH INST, H-1364 BUDAPEST, HUNGARY

[2] EOTVOS LORAND UNIV, DEPT COMP SCI, H-1088 BUDAPEST, HUNGARY

[3] PRINCETON UNIV, PRINCETON, NJ 08544 USA

[4] YALE UNIV, DEPT MATH, NEW HAVEN, CT 06520 USA

[5] YALE UNIV, COWLES FDN, NEW HAVEN, CT 06520 USA

来源：

COMBINATORICA | 1992年 / 12卷 / 02期

关键词：

AMS subject classification code (1991): 52C07; 11H06;

D O I：

10.1007/BF01204716

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a polyhedron P subset-of R(n) we write P(I) for the convex hull of the integral points in P. It is known that P(I) can have at most O(phi(n-1)) vertices if P is a rational polyhedron with size- phi. Here we give an example showing that P(I) can have as many as OMEGA(phi(n-1)) vertices. The construction uses the Dirichlet unit theorem.

引用

页码：135 / 142

页数：8

共 8 条

[1]

Borevich ZI, 1966, NUMBER THEORY

[2] ON INTEGER POINTS IN POLYHEDRA [J].