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指标为3的单纯Mendelsohn三元系大集
  • ISSN号：1673-0291
  • 期刊名称：《北京交通大学学报：自然科学版》
  • 时间：0
  • 分类：O157.2[理学—数学;理学—基础数学]
  • 作者机构：[1]北京交通大学理学院,北京100044
  • 相关基金：基金项目：国家自然科学基金资助项目（10771013;10831002）
作者： 范秉理[1]
关键词： 组合设计, 大集, MENDELSOHN三元系, 单纯, combinatorial design, large set , Mendelsohn triple system, pure
中文摘要：

一个指标为3的Mendelsohn三元系，记为MTS（v，3），是一个对子（X，B，其中X是一个v元集，B是X中循环三元组（区组）的集合，满足X的每一个有序对都恰包含于B中的3个区组．设（X，B是一个没有重复区组的MTS（v，3），如果（x，y，z）∈B必有（z，y，x）B则称（X，B为单纯的，记为PMTS（v，3）．不相交PMTS（v，3）大集，记为LPMTS（v，3），是一个集合（X，B）}i，其中每个（X，B）都是一个PMTS（v,3），并且UiBi构成了X中所有循环三元组的一个划分．本文给出了LPMTS（v，3）的一种构造方法，得到了其存在的一个无穷类：对于v=8，14（mod18），v≠14，存在LPMTS（v，3）．

英文摘要：

A Mendelsohn triple system of order v with index 3, briefly by MTS（v,3）, is a pair （X, B）, where X is a v-set and Bis a eolleetion of cyclie triples on X such that every ordered pair of X belongs to exactly 3 cyclic triples of 2.. A M TS（v,3） without repeated blocks is called pure and denoted by PMTS（ v ,3） if （ x, y, z） ∈Bimplies （ z, y, x） B. A large set of disjoint PMTS（ v ,3）, denoted by LPMTS（ v ,3）, is a collection t （ X ,Bi） }i, such that each （ X ,Bi） is a PMTS（ v ,3）, and U Bi is a partition of all cyclic triples on X. In this paper, we give a construction for LPMTS（ v ,3）, and obtain an infinite family for the existence of LPM T S（ v, 3）：for any v ≡8,14（mod 18）, v ≠ 14, there exists an LPMTS（v,3）.

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期刊信息
  • 《北京交通大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:北京交通大学
  • 主编：孙守光
  • 地址：北京市西直门外上园村3号北方交通大学8楼8101室
  • 邮编：100044
  • 邮箱：bfxb@bjtu.edu.cn
  • 电话：010-51688053
  • 国际标准刊号：ISSN：1673-0291
  • 国内统一刊号：ISSN：11-5258/U
  • 邮发代号:
  • 获奖情况:
  • 1995年铁道部科技期刊一等奖、1999年教育部组织的...
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  • 被引量:5152