一些非一次相关置换和对合的产生方法

Generation of Some Permutations and Involutions with Dependence Degree >1

本文讨论非一次相关置换和对合的产生问题．对于置换，首先给出了由给定置换进行仿射变换产生一类相关次数相同置换的方法，然后给出了由低维非一次相关置换递归产生高维非一次相关置换的方法，并估计了这些方法产生的置换个数．对于对合，给出了一个从特定非一次相关对合的不动点上构作不相交ｐ－组产生非一次相关对合的方法，并估计出一个对合个数的松下界．

In this paper, the authors deal with the generation of permutations and involutions with dependence degree >1. For permutation, they first give a method of generating a kind of permutations with the same dependence degree by affine transformations to a given permutation, then a recursive method of generating higher dimensional permutations from lower ones, and numbers of permutations generated by these methods are evaluated. For involution, the authors give a method of generating involutions with dependence degree >1 by making p disjoint transpositions with the same distance from fixed points of a given involution, and a loose lower bound of numbers of such generated involutions.