期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
A Type of 4-isosceles Set with 6-point
摘要/Abstract
摘要：
P为平面有限集(P⊆R2),称P为k-等腰的(k≥3):若P的每个k-子集均含有等腰三角形,即含有1个3元子集,其中1点到其他2点的距离相等.Fishburn提出是否存在无4点共圆、无3点共线的4-等腰6元集.现在就此问题构造一类无4点共圆的4等腰6元集和一类无4点共圆、无3点共线的4-等腰6元集.
Abstract：
Let P be a finite planar set. P is called a k-isosceles for k≥3,if every k-point subset of P contains a point equidistant from two others.Fishburn raised a problem that whether there exists a 4-isosceles 6-point with no 4-point on a circle and no 3-point on a line.The existences of 4-isosceles 6-point set with no 4-point on a circle and 4-isosceles 6-point set with no 4-point on a circle and no 3-point on a line are proved.
关键词
Key words：
k-isosceles
;
4-isosceles
;
4-point on a circle
;
3-point on a line