【摘要】 应用组合分析技巧,给出基于线排列与环形排列情形下的经典的Kaplansky计数命题的拓广情形,得到了两个推广后的新的Kaplansky计数命题.通过推广Ménage计数问题以及组合恒等式的证明,所得结果拓展了已有文献的研究结果.更多还原

【Abstract】 By using combinatorial analysis we extend Kaplansky enumerating theorems are to the general conditions under a linear permutation and a circular permutation.Two generalized theorems for the Kaplansky enumerating theorems are obtained.One class of Ménage enumerating problem is extended and some combinatorial identities are proved with the generalized Kaplansky enumerating theorems.Our results generalize those of the previous studies.更多还原