括号序列系统枚举之零
\[\mathrm{BrSS\ vs\ 1-Y}\]
\[\mathrm{BrSS:02\sim022}\]
\[\mathrm{1-Y:1,3\sim1,3,4,2,5,7,5}\]
记 \(\varphi = \frac{1+\sqrt{5}}{2}\),我们有 \(\varphi^2 = \varphi + 1\)。
定理: 设 \(p, q \in \mathbb{N}\),若 \(0<p<q\),则
\[ \begin{equation}\label{eq20241008_1} |\varphi - \frac{p}{q}| \gt \frac{1}{3q^2} \end{equation} \]