n元布尔函数的等价类计数方法

Counting Process for the Equivalence Classes of n-Variable Boolean Functions

讨论了ｎ元布尔函数在交换自变量顺序而其函数值不变意义下的等价类计数问题．利用置换群的轮换指标多项式和Ｐｏｌｙａ计数定理，得到具有相同重量的函数等价类的计数方法，并给出ｎ＝５的计算实例．

The counting problem for the equivalent classes of n-variable Boolean functions that have the same value after exchanging some order of the variables is discussed. Using the cyclic indexpolynomial of the permutation grop and Polya' s theorem, the counting process for equivalence classes of Boolean functions with the same weight is proposed. An example of applying the method with n=5 is illustrated.