具有固定得分向量的竞赛矩阵的数目  

On the Number of Tournaments with Prescribed Score Vector

作　　者：侯耀平[1] 

机构地区：[1]湖南师范大学数学系

出　　处：《数学学报（中文版）》2001年第1期111-116,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金!(19671013)

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．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.

关 键 词：竞赛矩阵 得分向量 计数 竞赛图 二重完全图 邻接矩阵 

分 类 号：O157.5[理学—数学]