Number of Balanced Functions - kipawaa/Proof-Tree GitHub Wiki
Statement
There are exactly ${n \choose \frac{n}{2}}$ Balanced Functions $f : \{0, 1\}^n \to \{0, 1\}$.
Explanation
Proof(s)
Let $f : \{0, 1\}^n \to \{0, 1\}$ be a Balanced Function.
Then we have that $\left\lvert\{x \in \{0, 1\}^n \mid f(x) = 0\}\right\rvert = \left\lvert\{x \in \{0, 1\}^n \mid f(x) = 1\}\right\rvert$.