奇数元平衡对称布尔函数的计数

The enumeration of symmetric balanced boolean functions with odd variables

目的对奇数元平衡布尔函数的奇数进行研究。方法利用组合数学理论。结果给出奇数n(n+3为完全平方数)元平衡对称布尔函数的计数下界。结论得到n为奇数时此类背包问题的非平凡解的充要条件,可以用来研究其他的布尔函数的计数。

Aim To investigate the enumeration of symmetric balanced Boolean functions with odd variables. Methods Using combinatorial theory. Results A lower bound on the enumeration of symmetric balanced Boolean function with odd n（ n ＋ 3 is a perfect square） variable is given. Conclusion A sufficient and necessary condition whether this knapsack problem has non-trivial solution is deduced, it is easy to apply this result to study other enumeration of Boolean functions.