journal6 ›› 2010, Vol. 31 ›› Issue (5): 1-4.

• 数学 •    下一篇

31阶Steiner三连系的构造与计数

  

  1. (1.安徽理工大学土木建筑学院,安徽 淮南232001;2.沈阳师范大学数学与系统科学学院,辽宁 沈阳110034)
  • 出版日期:2010-09-25 发布日期:2012-04-12
  • 作者简介:侴万禧(1930-),男,辽宁大连人,安徽理工大学教授,主要从事图论研究;李晓毅(1956-),女,辽宁葫芦岛人,沈阳师范大学教授,主要从事应用数学研究,E-mail:lixy@synu.edu.cn.
  • 基金资助:

    国家自然科学基金资助项目(10471096)

Construction and Enumeration of Steiner Triple System of Order

  1. (1.School of Civil Engineering and Architecture,Anhui University of Science and Technology,Huainan 232001,Anhui China;2.School of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)
  • Online:2010-09-25 Published:2012-04-12

摘要:阐明了v阶Steiner三连系构造的基本思路,给出了完全图Kv的边矩阵的定义,提出了2t+1阶Steiner三连系构造的一种方法.介绍了依据已存15阶Steiner三连系ST(15)构造31阶Steiner三连系的全过程,并讨论了2t+1阶Steiner三连系的计数问题.

关键词: Steiner三连系, 构造, 阶, 完全图, 边矩阵

Abstract: The basic concept of constructing Steiner triple system of order v is described.The definition of edge matrix of a complete graph Kv is given.A method of constructing Steiner triple system of order 2t+1 is proposed.The entire procedures of constructing Steiner triple system of order 31 according to the steiner triple system of order 15 is explicated.The enumeration problem of Steiner triple system is discussed.

Key words: Steiner triple system, construction, order, complete graph, edge matrix

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