【摘要】 循环赛的赛程安排是一类典型的排序问题.对于同一场地上的单循环赛程,以各队参赛的最小相隔场次作为赛程公平性的衡量指标,已有很多研究给出了构造一个最优解的方法.但是,尚没有对所有最优解所构成集合的探讨.针对这一问题,使用二元子集构成的序列表示赛程,将序列中相同元素的最小间隔定义为序列的分离度,并将具有最大分离度的序列定义为一个分离序列.通过分析分离序列所满足的性质,推出奇数阶二元子集的分离序列在同构意义下具有唯一性,并由一个一一映射给出其分段递归表达式.更多还原

【Abstract】 The schedule of round robin is a typical seqencing problem.For the single round robin on the same field,fairness of the scheduling is measured by the minimum interval between each team’s adjacent matches.So far various kinds of methods have been given to construct an optimal solution,however,there is no discussion on the set of all optimal solutions.Aiming at this problem,a sequence of binary subsets is raised to represent the schedule.The separation degree of the sequence is defined as the minimum interval of same elements,and a separation sequence is defined as a sequence with the maximum separation degree.By analyzing the properties of separation sequences,it is concluded that for odd order binary subsets,the structure of separation sequences is unique in the sense of isomorphism,and its piecewise recursive expression is given by a one to one mapping.更多还原