We show that the problem of counting the number of $n$-variable unate functions reduces to the problem of counting the number of $n$-variable monotone functions. Using recently obtained results on $n$-variable monotone functions, we obtain counts of $n$-variable unate functions up to $n=9$. We use an enumeration strategy to obtain the number of $n$-variable balanced monotone functions up to $n=7$. We show that the problem of counting the number of $n$-variable balanced unate functions reduces to the problem of counting the number of $n$-variable balanced monotone functions, and consequently, we obtain the number of $n$-variable balanced unate functions up to $n=7$. Using enumeration, we obtain the numbers of equivalence classes of $n$-variable balanced monotone functions, unate functions and balanced unate functions up to $n=6$. Further, for each of the considered sub-class of $n$-variable monotone and unate functions, we also obtain the corresponding numbers of $n$-variable non-degenerate functions.

翻译：我们证明了$n$变量单谷函数计数问题可归约为$n$变量单调函数计数问题。利用近期关于$n$变量单调函数的研究成果，我们获得了$n\leq 9$时$n$变量单谷函数的计数结果。采用枚举策略，我们得到了$n\leq 7$时$n$变量平衡单调函数的数量。研究表明，$n$变量平衡单谷函数计数问题可归约为$n$变量平衡单调函数计数问题，由此获得了$n\leq 7$时$n$变量平衡单谷函数的数量。通过枚举方法，我们得到了$n\leq 6$时$n$变量平衡单调函数、单谷函数及平衡单谷函数的等价类数量。此外，针对所考虑的$n$变量单调函数与单谷函数的每个子类，我们还得到了相应的$n$变量非退化函数数量。