| 具有固定得分向量的竞赛矩阵的数目 |
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| 引用本文： | 侯耀平. 具有固定得分向量的竞赛矩阵的数目[J]. 数学学报, 2001, 44(1): 111-116. DOI: cnki:ISSN:0583-1431.0.2001-01-014 |
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| 作者姓名： | 侯耀平 |
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| 作者单位： | 湖南师范大学数学系;中国科学技术大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目(19671013) |
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| 摘 要： | 本文考虑以允许平局的单循环比赛为模型的竞赛图（二重完全图）的定向图的邻接矩阵（竞赛矩阵）．给出了具有特殊得分向量的竞赛矩阵的数目，得到了具有ｎ阶强有效得分向量的竞赛矩阵的数目的下确界，并给出了达到此下界的得分向量的刻划．
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| 关 键 词： | 竞赛矩阵 得分向量 计数 |
| 文章编号： | 0583-1431(2001)01-0111-06 |
| 修稿时间： | 1998-11-18 |
On the Number of Tournaments with Prescribed Score Vector |
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| HOU Yao Ping. On the Number of Tournaments with Prescribed Score Vector[J]. Acta Mathematica Sinica, 2001, 44(1): 111-116. DOI: cnki:ISSN:0583-1431.0.2001-01-014 |
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| Authors: | HOU Yao Ping |
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| Affiliation: | HOU Yao Ping (Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China) (Department of Mathematics, University of Sicence and Technology of China, Hejei 230026, P. R. China) (E-mail: yphou@ustc.edn.cn) |
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| Abstract: | In this paper, we discuss the tournament matrix which can be interpreted as a competition where n participants play each other once in a match that can be end in ties. A player receives two points for each win and one point for each tie. We obtain the number of tournament matrices with special score vectors, and give the lower bound of the number for tournament matrices with strong score vectors and obtain the score vector with this lower bound. |
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| Keywords: | Tournament matrix Score vector Counter |
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