平行四边形的3-剖分

It has been proved that if a rectangle is dissected into three congruent pieces,then those pieces must themselves be rectangles. In the present paper this result is generalized to the case of parallelogram.     

Helly Type Problems forSome Special Convex Polygons

In the combinatorial geometry of convex sets the question of how efficiently a family ofconvex sets can be pierced by points has led to various problems which may be regarded asextensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviatedas n) if there exists a set of n points such that each member of the family contains at leastone of them. A family of sets is said to be nk: if every subfamily of size k or less is n. Thefamous Helly theorem in combinatorial …     

A Postscript on Erdoes－Szekeres Theorem

Let g(n) denote the least integer such that among any g(n) points in general position in the plane there are always n points in convex position.In this paper we show that g(n)≤(n-2 ↑2n-5) 2 by a new method.     

RESEARCH ANNOUNCEMENTS Helly Type Problems for Some Special Convex Polygons

In the combinatorial geometry of convex sets the question of how efficiently a family of convex sets can be pierced by points has led to various problems which may be regarded as extensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviated as Пn) if there exists a set of n points such that each member of the family contains at least one of them. A family of sets is said to be Пnk if every subfamily of size k or less is Пn. The famous Helly theorem in combinatorial geometry asserts that for finite families of convex sets in the plane П13 implies П1. In a recent paper by M. Katchalski and D. Nashtir[a] the following conjecture of Griinbaum[2] was mentioned again:     

一种特殊赋范空间中的Borsuk问题

Borsuk's problem is a famous problem in combinatorial geometry. It deals with the problem of partitioning a set into parts of smaller diameter. The problem was posed by the well-known Polish mathematician K. Borsuk in 1933. Many results have been obtained since then. In this paper, we discuss the Borsuk's problem in the normed space R^2 with regular hexagon as its unit sphere ∑ and obtain some new results.     

关于Erdos-Szekeres定理的一个注记

Let g(n) denote the least integer such that among any g(n) points in general position in the plane there are always n points in convex position. In this paper we show that g(n)≤(2n-5 , n-2)+2 by a new method.     

一类最小覆盖问题

对于任意给定的平行四边形,确定了与其相似的直径为1的三角形集族的最小平行四边形覆盖.     

Borsuk''''s Problem in a Special Normed Space

Borsuk's problem is a famous problem in combinatorial geometry. It deals with the problem of partitioning a set into parts of smaller diameter. The problem was posed by the well-known Polish mathematician K. Borsuk in 1933. Many results have been obtained since then. In this paper, we discuss the Borsuk's problem in the