| 不相交斯泰纳和柯克曼三元系大集两定理(一) |
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| 引用本文： | 罗洪田,王宇,孙晶,赵金伟.不相交斯泰纳和柯克曼三元系大集两定理(一)[J].数学的实践与认识,2009,39(21). |
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| 作者姓名： | 罗洪田 王宇 孙晶 赵金伟 |
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| 作者单位： | 1. 西安交通大学机械工程学院,西安,710048
2. 西安交通大学电信学院,西安,710048 |
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| 摘 要： | 给定一个斯泰纳或柯克曼三元系,介绍其大集的生成方法;得到其大集存在条件的判据是一个位差各异的循环数;柯克曼三元系其大集判据是,不能分解的柯克曼三元系有大集,能分解的无大集.
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| 关 键 词： | 斯泰纳三元系 柯克曼三元系 不能分解的柯克曼三元系 大集 循环数 位差 |
Two Theorems on Large Sets of Disjoint Steiner Triple System and Kirkman Triple System |
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| LUO Hong-tian,WANG Yu,SUN Jing,ZHAO Jin-wei.Two Theorems on Large Sets of Disjoint Steiner Triple System and Kirkman Triple System[J].Mathematics in Practice and Theory,2009,39(21). |
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| Authors: | LUO Hong-tian WANG Yu SUN Jing ZHAO Jin-wei |
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| Abstract: | We propose a method for generating large sets of a given Steiner triple system of order V, or of a given Kirkman triple system of order V, and obtain a sufficient condition for the existence of large sets in terms of cyclic numbers. This paper gives two theorems: Theoreml: A sufficient condition for the existence of large sets of Steiner triple systems S(V) and Kirkman triple systems K(V) is the existence of a cyclic number with totally different distances. Theorem2: There exist large sets for non-decomposable Kirkman triple systems and there exists no large set for a decomposable one. |
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| Keywords: | kirkman triple system steiner triple system non-decomposable kirkman triple system large set cyclic number distance |
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