SOME NOTES ABOUT AFFINE DIAMETERS OF CONVEX FIGURES

被引：1

作者：

SOLTAN, VP ^{[1
]}

HUNG, NM ^{[1
]}

机构：

[1] INST MATH MECH,KISHINEV 277028,USSR

来源：

COMBINATORICA | 1990年 / 10卷 / 03期

关键词：

AMS subject classification (1980): 52A30; 52A40;

D O I：

10.1007/BF02122784

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a point x in a convex figure M, let gamma(x) denote the number of all affine diameters of M passing through x. It is shown that, for a convex figure M, the following conditions are equivalent. (i) gamma(x) greater-than-or-equal-to 2 for every point x is-an-element-of int M. (ii) either gamma(x) = 3 or gamma(x) = infinity on int M. Furthermore, the set B = {x is-an-element-of int M: gamma(x) is either odd or infinite} is dense in M.

引用

页码：313 / 317

页数：5